Bulletin of the American Physical Society, Mar 3, 2020
We predict magnetization plateaus ground states for S = 1/2 Heisenberg antiferromagnets on pyroch... more We predict magnetization plateaus ground states for S = 1/2 Heisenberg antiferromagnets on pyrochlore lattices by formulating arguments based on gauge and spin-parity transformations. We derive a twist operator appropriate to the pyrochlore lattice, and show that it is equivalent to a large gauge transformation. Invariance under this large gauge transformation indicates the sensitivity of the ground state to changes in boundary conditions. This leads to the formulation of an Oshikawa-Yamanaka-Affleck-like criterion at finite external magnetic field, enabling the prediction of plateaus in the magnetization versus field diagram. We also develop an analysis based on the spin-parity operator, leading to a condition from which identical predictions are obtained of magnetization plateaus ground states. Both analyses are based on the non-local nature of the transformations, and rely only on the symmetries of the Hamiltonian. This suggests that the plateaus ground states can possess properties arising from non-local entanglement between the spins.
With a brief introduction to one-dimensional channels and conductance quantisation in mesoscopic ... more With a brief introduction to one-dimensional channels and conductance quantisation in mesoscopic systems, we discuss some recent experimental puzzles in these systems, which include reduction of quantised conductances and an interesting odd-even effect in the presence of an in-plane magnetic field. We then discuss a recent non-homogeneous Luttinger liquid model proposed by us, which addresses and gives an explanation for the reduced conductances and the odd-even effect. We end with a brief summary and discussion of future projects.
We present a T = 0K renormalization group (RG) phase diagram for the electronic Hubbard model in ... more We present a T = 0K renormalization group (RG) phase diagram for the electronic Hubbard model in two dimensions on the square lattice at, and away from, half filling. The RG procedure treats quantum fluctuations in the single particle occupation number nonperturbatively via the unitarily decoupling of one electronic state at every RG step. The resulting phase diagram thus possess the quantum fluctuation energy scale (ω) as one of its axes. A relation is derived between ω and the effective temperature scale upto which gapless, as well as emergent gapped, phases can be obtained. We find that the transition in the half-filled Hubbard model involves, for any on-site repulsion, passage from a marginal Fermi liquid to a topologically-ordered gapped Mott liquid through a pseudogapped phase bookended by Fermi surface topology-changing Lifshitz transitions. Using effective Hamiltonians and wavefunctions for the low-energy many-body eigenstates for the doped Mott liquid obtained from the stable fixed point of the RG flow, we demonstrate the collapse of the pseudogap for charge excitations (Mottness) at a quantum critical point possessing a nodal non-Fermi liquid with superconducting fluctuations, and spin-pseudogapping near the antinodes. d-wave Superconducting order is shown to arise from this quantum critical state of matter. Benchmarking of the ground state energy per particle and the double-occupancy fraction against existing numerical results also yields excellent agreement. We present detailed insight into the T = 0 origin of several experimentally observed findings in the cuprates, including Homes law and Planckian dissipation. We also establish that the heirarchy of temperature scales for the pseudogap (TP G), onset temperature for pairing (Tons), formation of the Mott liquid (TML) and superconductivity (TC ) obtained from our analysis is quantitatively consistent with that observed experimentally for some members of the cuprates. Our results offer insight on the ubiquitous origin of superconductivity in doped Mott insulating states, and pave the way towards a systematic search for higher superconducting transition temperatures in such systems.
Bulletin of the American Physical Society, Mar 5, 2018
Motivated by recent experiments, we present a comprehensive theoretical study of the geometricall... more Motivated by recent experiments, we present a comprehensive theoretical study of the geometrically frustrated strongly correlated magnetic insulator Mn3O4 spinel oxide based on a microscopic Hamiltonian involving lattice, spin and orbital degrees of freedom. Possessing the physics of degenerate eg orbitals, this system shows a strong Jahn-Teller effect at high temperatures. Further, careful attention is paid to the special nature of the superexchange physics arising from the 90 o Mn-O-Mn bonding angle. The Jahn-Teller and superexchange-based orbital-spin Hamiltonians are then analysed in order to track the dynamics of orbital and spin ordering. We find that a high-temperature structural transition results in orbital ordering whose nature is mixed with respect to the two originally degenerate eg orbitals. This ordering of orbitals is shown to relieve the intrinsic geometric frustration of the spins on the spinel lattice, leading to ferrimagnetic Yafet-Kittel ordering at lowtemperatures. Finally, we develop a model for a magnetoelastic coupling in Mn3O4, enabling a systematic understanding of the experimentally observed complexity in the low-temperature structural and magnetic phenomenology of this spinel. Our analysis predicts that a quantum fluctuation-driven orbital-spin liquid phase may be stabilised at low temperatures upon the application of pressure.
Bulletin of the American Physical Society, Mar 19, 2010
Charge Fractionalization in a Mesoscopic Ring WADE DEGOT-TARDI, SIDDHARTHA LAL, SMITHA VISHVESHWA... more Charge Fractionalization in a Mesoscopic Ring WADE DEGOT-TARDI, SIDDHARTHA LAL, SMITHA VISHVESHWARA, University of Illinois at Urbana-Champaign -In interacting one-dimensional systems, Luttinger liquid theory predicts the existence of fractionally charged quasiparticles whose properties depend on the Luttinger parameter. Recent experiments performed on quantum wires suggest the observation of such fractionalization. A complication that needs to be carefully considered in these geometries is that all measurements ultimately involve electrons that have tunneled outside the one-dimensional system into leads. Here, we propose a means of bypassing this complication by introducing a ring geometry and focusing on the non-invasive measurement of the time averaged power dissipated in a pickup loop proximate to the ring. We show that signatures of fractionalization of an electron that has tunneled into the ring are present in the dissipated power profile around the ring. As an independent measurement, we also show that the Luttinger parameter in the ring geometry can be derived from Coulomb blockade resonances controlled by both a tunable chemical potential and an Aharonov-Bohm flux.
We study transport in a model of a quantum Hall edge system with a gate-voltage controlled constr... more We study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a Landauer-Buttiker analysis as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk (ν 1 ) and constriction (ν 2 ) quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. These findings provide satisfactory explanations for several puzzling recent experimental results. These results are confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with some of the recent puzzling experimental results for the cases of ν 1 = 1/3, 1.
An outstanding challenge involves understanding the many-particle entanglement of liquid states o... more An outstanding challenge involves understanding the many-particle entanglement of liquid states of quantum matter that arise in systems of interacting electrons. The Fermi liquid (FL) shows a violation of the area-law in real-space entanglement entropy of a subsystem, believed to be a signature of the ground state of a gapless quantum critical system of interacting fermions. Here, we apply a T = 0 renormalization group approach to the FL, unveiling the long-wavelength quantum fluctuations from which long-range entanglement arises. A similar analysis of non-Fermi liquids such as the 2D marginal Fermi liquid (MFL) and the 1D Tomonaga–Luttinger liquid reveals a universal logarithmic violation of the area-law in gapless electronic liquids, with a proportionality constant that depends on the nature of the underlying Fermi surface. We extend this analysis to classify the gapped quantum liquids emergent from the destabilisation of the Fermi surface by renormalisation group relevant quantum fluctuations arising from backscattering processes.
Pressure-dependent, low temperature inelastic light (Raman) scattering measurements of KCuF3 show... more Pressure-dependent, low temperature inelastic light (Raman) scattering measurements of KCuF3 show that applied pressure above P * ∼ 7 kbar suppresses a previously observed structural phase transition temperature to zero temperature in KCuF3, resulting in the development of a ω ∼ 0 fluctuational (quasielastic) response near T ∼ 0 K. This pressure-induced fluctuational response -which we associate with slow fluctuations of the CuF6 octahedral orientation -is temperature independent and exhibits a characteristic fluctuation rate that is much larger than the temperature, consistent with quantum fluctuations of the CuF6 octahedra. A model of pseudospin-phonon coupling provides a qualitative description of both the temperature-and pressure-dependent evolution of the Raman spectra of KCuF3.
With the motivation of overcoming difficulties in studying systems of several one dimensional Tom... more With the motivation of overcoming difficulties in studying systems of several one dimensional Tomonaga Luttinger liquid wires connected locally at a junction, we construct quadratic lattice field theories for the single non-chiral/chiral wire, the three wire fork and the chiral box junction. For a fork consisting of three identical non-chiral wires, we find that the permutation symmetries of the system, together with the requirement of charge and current continuity, determine the terms in the action governing the dynamics of the fields adjacent to the junction. These results are generalised to the case of N ≥ 3 identical (as well as different) TLL wires. A study of the chiral box junction circuit model reveals that junctions of several chiral wires can be formed by relating the TLL interaction parameters of their constituents.
We study transport in a model of a quantum Hall edge system with a gate-voltage controlled constr... more We study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a Landauer-Buttiker analysis as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk (ν 1 ) and constriction (ν 2 ) quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. These findings provide satisfactory explanations for several puzzling recent experimental results. These results are confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with some of the recent puzzling experimental results for the cases of ν 1 = 1/3, 1.
We consider the problem of competing orders in a stripe phase with a large spin gap. In developin... more We consider the problem of competing orders in a stripe phase with a large spin gap. In developing the phase diagram, we discuss the phases arising from the stabilization of the Superconducting (SC) and Charge Density Wave (CDW) orders by inter-stripe couplings. This is ...
We discuss results on single layer graphene junctions made by a graphene sheet in contact with a ... more We discuss results on single layer graphene junctions made by a graphene sheet in contact with a superconducting tunnel probe and a normal ohmic contact. The superconducting gap of the tunnel probes is well formed at 250 mK. However, we observe an additional ...
With the motivation of overcoming difficulties in studying systems of several one dimensional Tom... more With the motivation of overcoming difficulties in studying systems of several one dimensional Tomonaga Luttinger liquid wires connected locally at a junction, we construct quadratic lattice field theories for the single non-chiral/chiral wire, the three wire fork and the chiral box junction. For a fork consisting of three identical non-chiral wires, we find that the permutation symmetries of the system, together with the requirement of charge and current continuity, determine the terms in the action governing the dynamics of the fields adjacent to the junction. These results are generalised to the case of N ≥ 3 identical (as well as different) TLL wires. A study of the chiral box junction circuit model reveals that junctions of several chiral wires can be formed by relating the TLL interaction parameters of their constituents.
Motivated by surprises in recent experimental findings, we study transport in a model of a quantu... more Motivated by surprises in recent experimental findings, we study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk (ν 1 ) and constriction (ν 2 ) quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. The competition between two interedge tunneling processes taking place inside the constriction, related by a quasiparticlequasihole (qp-qh) symmetry, is accounted for by computing the boundary theories of the system. This competition is found to determine the strong coupling configuration of the system. A separatrix of qp-qh symmetric gapless critical states is found to lie between the relevant RG flows to a metallic and an insulating configuration of the constriction system. This constitutes an interesting generalisation of the Kane-Fisher quantum impurity model. The features of the RG phase diagram are also confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with many recent puzzling experimental results for the cases of ν 1 = 1/3, 1. We also discuss and make predictions for the case of a constriction system with ν 2 = 5/2.
Elucidating the emergence of long-range magnetic ordering from its precursor short-range magnetic... more Elucidating the emergence of long-range magnetic ordering from its precursor short-range magnetic ordering (SRMO) in two-dimensional van der Waals materials holds profound implications for fundamental research and technological advancements. However, directly observing the intricate stages of this magnetic dimensional crossover (MDC) remains a significant experimental challenge. While magneto-elastic coupling offers a promising avenue, detecting the minute lattice response to SRMO proves challenging. Recent investigations utilizing second harmonic generation have unveiled a two-step MDC in a van der Waals ferromagnetic insulator. However, an unambiguous detection of MDC through the time-resolved techniques remains elusive. To meet this goal, we have executed an alternative approach by employing picosecond acoustic strain pulses generated by femtosecond lasers to probe the various stages of MDC through the magneto-elastic coupling for the first time. By analyzing the shape of the strain pulse in both the time and frequency domains as a function of temperature, we clearly demonstrate the detection of the subtle influence of spin fluctuations on the lattice. Additionally, the ultrafast carrier dynamics also show signatures of MDC. Our measurements pave the way towards characterizing magnetic materials in time-resolved experiments that are crucial in designing a new generation of spin-based optoelectronic devices.
We study the spectrum of fermions hopping on a chain with a weak incommensuration close to dimeri... more We study the spectrum of fermions hopping on a chain with a weak incommensuration close to dimerization; both q, the deviation of the wave number from π, and δ, the strength of the incommensuration, are small. For free fermions, we use a continuum Dirac theory to show that there are an infinite number of bands which meet at zero energy as q approaches zero. In the limit that the ratio q/δ → 0, the number of states lying inside the q = 0 gap is nonzero and equal to 2δ/π 2. Thus the limit q → 0 differs from q = 0; this can be seen clearly in the behavior of the specific heat at low temperature. For interacting fermions or the XXZ spin-1/2 chain close to dimerization, we use bosonization to argue that similar results hold; as q → 0, we find a nontrivial density of states near zero energy. However, the limit q → 0 and q = 0 give the same results near commensurate wave numbers which are different from π. We apply our results to the Azbel-Hofstadter problem of electrons hopping on a two-dimensional lattice in the presence of a magnetic field. Finally, we discuss the complete energy spectrum of noninteracting fermions with incommensurate hopping by going up to higher orders in δ.
We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary re... more We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary renormalization group (URG) technique. Our results display the importance of ground state degeneracy in explaining various important properties like the breakdown of screening and the presence of local non-Fermi liquids. The impurity susceptibility of the intermediate coupling fixed point Hamiltonian in the zero-bandwidth (or star graph) limit shows a power-law divergence at low temperature. Despite the absence of interchannel coupling in the MCK fixed point Hamiltonian, the study of mutual information between any two channels shows non-zero correlation between them. A spectral flow analysis of the star graph reveals that the degenerate ground state manifold possesses topological quantum numbers. Upon disentangling the impurity spin from its partners in the star graph, we find the presence of a local Mott liquid arising from inter-channel scattering processes. The low energy effective Hamiltonian obtained upon adding a finite non-zero conduction bath dispersion to the star graph Hamiltonian for both the two and three-channel cases displays the presence of local non-Fermi liquids arising from inter-channel quantum fluctuations. Specifically, we confirm the presence of a local marginal Fermi liquid in the two channel case, whose properties show logarithmic scaling at low temperature as expected. Discontinuous behaviour is observed in several measures of ground state entanglement, signalling the underlying orthogonality catastrophe associated with the degenerate ground state manifold. We extend our results to underscreened and perfectly screened MCK models through duality arguments. A study of channel anisotropy under renormalisation flow reveals a series of quantum phase transitions due to the change in ground state degeneracy. Our work thus presents a template for the study of how a degenerate ground state manifold arising from symmetry and duality properties in a multichannel quantum impurity model can lead to novel multicritical phases at intermediate coupling.
We analyze the single-channel Kondo model using the recently developed unitary renormalisation gr... more We analyze the single-channel Kondo model using the recently developed unitary renormalisation group (URG) method, and obtain a comprehensive understanding of the Kondo screening cloud. The fixed-point low-energy Hamiltonian enables the computation of a plethora of thermodynamic quantities (specific heat, susceptibility, Wilson ratio, etc.) as well as spectral functions, all of which are found to be in good agreement with known results. By integrating out the impurity, we obtain an effective Hamiltonian for the excitations of the electrons comprising the Kondo cloud. This is found to contain both k−space number-diagonal (Fermi liquid) as well off-diagonal four-fermion scattering terms. Our conclusions are reinforced by a URG study of the two-particle entanglement and manybody correlations among members of the Kondo cloud and impurity. The entanglement between the impurity and a cloud electron, as well as between any two cloud electrons, is found to increase under flow towards the singlet ground state at the strong-coupling fixed point. Both the number-diagonal and off-diagonal correlations within the conduction cloud are also found to increase as the impurity is screened under the flow, and the latter are found to be responsible for the macroscopic entanglement of the Kondo-singlet ground state. The unitary RG flow enables an analytic computation of the phase shifts suffered by the conduction electrons at the strong-coupling fixed point. This reveals an orthogonality catastrophe between the local moment and strong-coupling ground states, and is related to a change in the Luttinger volume of the conduction bath under the crossover to strong coupling. Our results offer fresh insight on the nature of the emergent many-particle entanglement within the Kondo cloud, and pave the way for further investigations in more exotic contexts such as the fixed point of the over-screened multi-channel Kondo problem.
Bulletin of the American Physical Society, Mar 3, 2020
We predict magnetization plateaus ground states for S = 1/2 Heisenberg antiferromagnets on pyroch... more We predict magnetization plateaus ground states for S = 1/2 Heisenberg antiferromagnets on pyrochlore lattices by formulating arguments based on gauge and spin-parity transformations. We derive a twist operator appropriate to the pyrochlore lattice, and show that it is equivalent to a large gauge transformation. Invariance under this large gauge transformation indicates the sensitivity of the ground state to changes in boundary conditions. This leads to the formulation of an Oshikawa-Yamanaka-Affleck-like criterion at finite external magnetic field, enabling the prediction of plateaus in the magnetization versus field diagram. We also develop an analysis based on the spin-parity operator, leading to a condition from which identical predictions are obtained of magnetization plateaus ground states. Both analyses are based on the non-local nature of the transformations, and rely only on the symmetries of the Hamiltonian. This suggests that the plateaus ground states can possess properties arising from non-local entanglement between the spins.
With a brief introduction to one-dimensional channels and conductance quantisation in mesoscopic ... more With a brief introduction to one-dimensional channels and conductance quantisation in mesoscopic systems, we discuss some recent experimental puzzles in these systems, which include reduction of quantised conductances and an interesting odd-even effect in the presence of an in-plane magnetic field. We then discuss a recent non-homogeneous Luttinger liquid model proposed by us, which addresses and gives an explanation for the reduced conductances and the odd-even effect. We end with a brief summary and discussion of future projects.
We present a T = 0K renormalization group (RG) phase diagram for the electronic Hubbard model in ... more We present a T = 0K renormalization group (RG) phase diagram for the electronic Hubbard model in two dimensions on the square lattice at, and away from, half filling. The RG procedure treats quantum fluctuations in the single particle occupation number nonperturbatively via the unitarily decoupling of one electronic state at every RG step. The resulting phase diagram thus possess the quantum fluctuation energy scale (ω) as one of its axes. A relation is derived between ω and the effective temperature scale upto which gapless, as well as emergent gapped, phases can be obtained. We find that the transition in the half-filled Hubbard model involves, for any on-site repulsion, passage from a marginal Fermi liquid to a topologically-ordered gapped Mott liquid through a pseudogapped phase bookended by Fermi surface topology-changing Lifshitz transitions. Using effective Hamiltonians and wavefunctions for the low-energy many-body eigenstates for the doped Mott liquid obtained from the stable fixed point of the RG flow, we demonstrate the collapse of the pseudogap for charge excitations (Mottness) at a quantum critical point possessing a nodal non-Fermi liquid with superconducting fluctuations, and spin-pseudogapping near the antinodes. d-wave Superconducting order is shown to arise from this quantum critical state of matter. Benchmarking of the ground state energy per particle and the double-occupancy fraction against existing numerical results also yields excellent agreement. We present detailed insight into the T = 0 origin of several experimentally observed findings in the cuprates, including Homes law and Planckian dissipation. We also establish that the heirarchy of temperature scales for the pseudogap (TP G), onset temperature for pairing (Tons), formation of the Mott liquid (TML) and superconductivity (TC ) obtained from our analysis is quantitatively consistent with that observed experimentally for some members of the cuprates. Our results offer insight on the ubiquitous origin of superconductivity in doped Mott insulating states, and pave the way towards a systematic search for higher superconducting transition temperatures in such systems.
Bulletin of the American Physical Society, Mar 5, 2018
Motivated by recent experiments, we present a comprehensive theoretical study of the geometricall... more Motivated by recent experiments, we present a comprehensive theoretical study of the geometrically frustrated strongly correlated magnetic insulator Mn3O4 spinel oxide based on a microscopic Hamiltonian involving lattice, spin and orbital degrees of freedom. Possessing the physics of degenerate eg orbitals, this system shows a strong Jahn-Teller effect at high temperatures. Further, careful attention is paid to the special nature of the superexchange physics arising from the 90 o Mn-O-Mn bonding angle. The Jahn-Teller and superexchange-based orbital-spin Hamiltonians are then analysed in order to track the dynamics of orbital and spin ordering. We find that a high-temperature structural transition results in orbital ordering whose nature is mixed with respect to the two originally degenerate eg orbitals. This ordering of orbitals is shown to relieve the intrinsic geometric frustration of the spins on the spinel lattice, leading to ferrimagnetic Yafet-Kittel ordering at lowtemperatures. Finally, we develop a model for a magnetoelastic coupling in Mn3O4, enabling a systematic understanding of the experimentally observed complexity in the low-temperature structural and magnetic phenomenology of this spinel. Our analysis predicts that a quantum fluctuation-driven orbital-spin liquid phase may be stabilised at low temperatures upon the application of pressure.
Bulletin of the American Physical Society, Mar 19, 2010
Charge Fractionalization in a Mesoscopic Ring WADE DEGOT-TARDI, SIDDHARTHA LAL, SMITHA VISHVESHWA... more Charge Fractionalization in a Mesoscopic Ring WADE DEGOT-TARDI, SIDDHARTHA LAL, SMITHA VISHVESHWARA, University of Illinois at Urbana-Champaign -In interacting one-dimensional systems, Luttinger liquid theory predicts the existence of fractionally charged quasiparticles whose properties depend on the Luttinger parameter. Recent experiments performed on quantum wires suggest the observation of such fractionalization. A complication that needs to be carefully considered in these geometries is that all measurements ultimately involve electrons that have tunneled outside the one-dimensional system into leads. Here, we propose a means of bypassing this complication by introducing a ring geometry and focusing on the non-invasive measurement of the time averaged power dissipated in a pickup loop proximate to the ring. We show that signatures of fractionalization of an electron that has tunneled into the ring are present in the dissipated power profile around the ring. As an independent measurement, we also show that the Luttinger parameter in the ring geometry can be derived from Coulomb blockade resonances controlled by both a tunable chemical potential and an Aharonov-Bohm flux.
We study transport in a model of a quantum Hall edge system with a gate-voltage controlled constr... more We study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a Landauer-Buttiker analysis as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk (ν 1 ) and constriction (ν 2 ) quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. These findings provide satisfactory explanations for several puzzling recent experimental results. These results are confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with some of the recent puzzling experimental results for the cases of ν 1 = 1/3, 1.
An outstanding challenge involves understanding the many-particle entanglement of liquid states o... more An outstanding challenge involves understanding the many-particle entanglement of liquid states of quantum matter that arise in systems of interacting electrons. The Fermi liquid (FL) shows a violation of the area-law in real-space entanglement entropy of a subsystem, believed to be a signature of the ground state of a gapless quantum critical system of interacting fermions. Here, we apply a T = 0 renormalization group approach to the FL, unveiling the long-wavelength quantum fluctuations from which long-range entanglement arises. A similar analysis of non-Fermi liquids such as the 2D marginal Fermi liquid (MFL) and the 1D Tomonaga–Luttinger liquid reveals a universal logarithmic violation of the area-law in gapless electronic liquids, with a proportionality constant that depends on the nature of the underlying Fermi surface. We extend this analysis to classify the gapped quantum liquids emergent from the destabilisation of the Fermi surface by renormalisation group relevant quantum fluctuations arising from backscattering processes.
Pressure-dependent, low temperature inelastic light (Raman) scattering measurements of KCuF3 show... more Pressure-dependent, low temperature inelastic light (Raman) scattering measurements of KCuF3 show that applied pressure above P * ∼ 7 kbar suppresses a previously observed structural phase transition temperature to zero temperature in KCuF3, resulting in the development of a ω ∼ 0 fluctuational (quasielastic) response near T ∼ 0 K. This pressure-induced fluctuational response -which we associate with slow fluctuations of the CuF6 octahedral orientation -is temperature independent and exhibits a characteristic fluctuation rate that is much larger than the temperature, consistent with quantum fluctuations of the CuF6 octahedra. A model of pseudospin-phonon coupling provides a qualitative description of both the temperature-and pressure-dependent evolution of the Raman spectra of KCuF3.
With the motivation of overcoming difficulties in studying systems of several one dimensional Tom... more With the motivation of overcoming difficulties in studying systems of several one dimensional Tomonaga Luttinger liquid wires connected locally at a junction, we construct quadratic lattice field theories for the single non-chiral/chiral wire, the three wire fork and the chiral box junction. For a fork consisting of three identical non-chiral wires, we find that the permutation symmetries of the system, together with the requirement of charge and current continuity, determine the terms in the action governing the dynamics of the fields adjacent to the junction. These results are generalised to the case of N ≥ 3 identical (as well as different) TLL wires. A study of the chiral box junction circuit model reveals that junctions of several chiral wires can be formed by relating the TLL interaction parameters of their constituents.
We study transport in a model of a quantum Hall edge system with a gate-voltage controlled constr... more We study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained from a Landauer-Buttiker analysis as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk (ν 1 ) and constriction (ν 2 ) quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. These findings provide satisfactory explanations for several puzzling recent experimental results. These results are confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with some of the recent puzzling experimental results for the cases of ν 1 = 1/3, 1.
We consider the problem of competing orders in a stripe phase with a large spin gap. In developin... more We consider the problem of competing orders in a stripe phase with a large spin gap. In developing the phase diagram, we discuss the phases arising from the stabilization of the Superconducting (SC) and Charge Density Wave (CDW) orders by inter-stripe couplings. This is ...
We discuss results on single layer graphene junctions made by a graphene sheet in contact with a ... more We discuss results on single layer graphene junctions made by a graphene sheet in contact with a superconducting tunnel probe and a normal ohmic contact. The superconducting gap of the tunnel probes is well formed at 250 mK. However, we observe an additional ...
With the motivation of overcoming difficulties in studying systems of several one dimensional Tom... more With the motivation of overcoming difficulties in studying systems of several one dimensional Tomonaga Luttinger liquid wires connected locally at a junction, we construct quadratic lattice field theories for the single non-chiral/chiral wire, the three wire fork and the chiral box junction. For a fork consisting of three identical non-chiral wires, we find that the permutation symmetries of the system, together with the requirement of charge and current continuity, determine the terms in the action governing the dynamics of the fields adjacent to the junction. These results are generalised to the case of N ≥ 3 identical (as well as different) TLL wires. A study of the chiral box junction circuit model reveals that junctions of several chiral wires can be formed by relating the TLL interaction parameters of their constituents.
Motivated by surprises in recent experimental findings, we study transport in a model of a quantu... more Motivated by surprises in recent experimental findings, we study transport in a model of a quantum Hall edge system with a gate-voltage controlled constriction. A finite backscattered current at finite edge-bias is explained as arising from the splitting of edge current caused by the difference in the filling fractions of the bulk (ν 1 ) and constriction (ν 2 ) quantum Hall fluid regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model. The constriction region splits the incident long-wavelength chiral edge density-wave excitations among the transmitting and reflecting edge states encircling it. The competition between two interedge tunneling processes taking place inside the constriction, related by a quasiparticlequasihole (qp-qh) symmetry, is accounted for by computing the boundary theories of the system. This competition is found to determine the strong coupling configuration of the system. A separatrix of qp-qh symmetric gapless critical states is found to lie between the relevant RG flows to a metallic and an insulating configuration of the constriction system. This constitutes an interesting generalisation of the Kane-Fisher quantum impurity model. The features of the RG phase diagram are also confirmed by computing various correlators and chiral linear conductances of the system. In this way, our results find excellent agreement with many recent puzzling experimental results for the cases of ν 1 = 1/3, 1. We also discuss and make predictions for the case of a constriction system with ν 2 = 5/2.
Elucidating the emergence of long-range magnetic ordering from its precursor short-range magnetic... more Elucidating the emergence of long-range magnetic ordering from its precursor short-range magnetic ordering (SRMO) in two-dimensional van der Waals materials holds profound implications for fundamental research and technological advancements. However, directly observing the intricate stages of this magnetic dimensional crossover (MDC) remains a significant experimental challenge. While magneto-elastic coupling offers a promising avenue, detecting the minute lattice response to SRMO proves challenging. Recent investigations utilizing second harmonic generation have unveiled a two-step MDC in a van der Waals ferromagnetic insulator. However, an unambiguous detection of MDC through the time-resolved techniques remains elusive. To meet this goal, we have executed an alternative approach by employing picosecond acoustic strain pulses generated by femtosecond lasers to probe the various stages of MDC through the magneto-elastic coupling for the first time. By analyzing the shape of the strain pulse in both the time and frequency domains as a function of temperature, we clearly demonstrate the detection of the subtle influence of spin fluctuations on the lattice. Additionally, the ultrafast carrier dynamics also show signatures of MDC. Our measurements pave the way towards characterizing magnetic materials in time-resolved experiments that are crucial in designing a new generation of spin-based optoelectronic devices.
We study the spectrum of fermions hopping on a chain with a weak incommensuration close to dimeri... more We study the spectrum of fermions hopping on a chain with a weak incommensuration close to dimerization; both q, the deviation of the wave number from π, and δ, the strength of the incommensuration, are small. For free fermions, we use a continuum Dirac theory to show that there are an infinite number of bands which meet at zero energy as q approaches zero. In the limit that the ratio q/δ → 0, the number of states lying inside the q = 0 gap is nonzero and equal to 2δ/π 2. Thus the limit q → 0 differs from q = 0; this can be seen clearly in the behavior of the specific heat at low temperature. For interacting fermions or the XXZ spin-1/2 chain close to dimerization, we use bosonization to argue that similar results hold; as q → 0, we find a nontrivial density of states near zero energy. However, the limit q → 0 and q = 0 give the same results near commensurate wave numbers which are different from π. We apply our results to the Azbel-Hofstadter problem of electrons hopping on a two-dimensional lattice in the presence of a magnetic field. Finally, we discuss the complete energy spectrum of noninteracting fermions with incommensurate hopping by going up to higher orders in δ.
We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary re... more We study the overscreened multi-channel Kondo (MCK) model using the recently developed unitary renormalization group (URG) technique. Our results display the importance of ground state degeneracy in explaining various important properties like the breakdown of screening and the presence of local non-Fermi liquids. The impurity susceptibility of the intermediate coupling fixed point Hamiltonian in the zero-bandwidth (or star graph) limit shows a power-law divergence at low temperature. Despite the absence of interchannel coupling in the MCK fixed point Hamiltonian, the study of mutual information between any two channels shows non-zero correlation between them. A spectral flow analysis of the star graph reveals that the degenerate ground state manifold possesses topological quantum numbers. Upon disentangling the impurity spin from its partners in the star graph, we find the presence of a local Mott liquid arising from inter-channel scattering processes. The low energy effective Hamiltonian obtained upon adding a finite non-zero conduction bath dispersion to the star graph Hamiltonian for both the two and three-channel cases displays the presence of local non-Fermi liquids arising from inter-channel quantum fluctuations. Specifically, we confirm the presence of a local marginal Fermi liquid in the two channel case, whose properties show logarithmic scaling at low temperature as expected. Discontinuous behaviour is observed in several measures of ground state entanglement, signalling the underlying orthogonality catastrophe associated with the degenerate ground state manifold. We extend our results to underscreened and perfectly screened MCK models through duality arguments. A study of channel anisotropy under renormalisation flow reveals a series of quantum phase transitions due to the change in ground state degeneracy. Our work thus presents a template for the study of how a degenerate ground state manifold arising from symmetry and duality properties in a multichannel quantum impurity model can lead to novel multicritical phases at intermediate coupling.
We analyze the single-channel Kondo model using the recently developed unitary renormalisation gr... more We analyze the single-channel Kondo model using the recently developed unitary renormalisation group (URG) method, and obtain a comprehensive understanding of the Kondo screening cloud. The fixed-point low-energy Hamiltonian enables the computation of a plethora of thermodynamic quantities (specific heat, susceptibility, Wilson ratio, etc.) as well as spectral functions, all of which are found to be in good agreement with known results. By integrating out the impurity, we obtain an effective Hamiltonian for the excitations of the electrons comprising the Kondo cloud. This is found to contain both k−space number-diagonal (Fermi liquid) as well off-diagonal four-fermion scattering terms. Our conclusions are reinforced by a URG study of the two-particle entanglement and manybody correlations among members of the Kondo cloud and impurity. The entanglement between the impurity and a cloud electron, as well as between any two cloud electrons, is found to increase under flow towards the singlet ground state at the strong-coupling fixed point. Both the number-diagonal and off-diagonal correlations within the conduction cloud are also found to increase as the impurity is screened under the flow, and the latter are found to be responsible for the macroscopic entanglement of the Kondo-singlet ground state. The unitary RG flow enables an analytic computation of the phase shifts suffered by the conduction electrons at the strong-coupling fixed point. This reveals an orthogonality catastrophe between the local moment and strong-coupling ground states, and is related to a change in the Luttinger volume of the conduction bath under the crossover to strong coupling. Our results offer fresh insight on the nature of the emergent many-particle entanglement within the Kondo cloud, and pave the way for further investigations in more exotic contexts such as the fixed point of the over-screened multi-channel Kondo problem.
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Papers by Siddhartha Lal