Papers by Abdollah Langari
We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ) on the an... more We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ) on the antiferromagnetic J1 -J2 Ising model on the checkerboard lattice, the two dimensional version of the pyrochlore lattice. The zero-temperature phase diagram of the model has been obtained by employing a plaquette operator approach (POA). The plaquette operator formalism bosonizes the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a plaquette ordered solid (RPS) state, which breaks lattice translational symmetry, in addition to a unique collinear phase for J2 > J1. The bosonic excitation gap vanishes at the critical points to the Néel (J2 < J1) and collinear (J2 > J1) ordered phases, which defines the critical phase boundaries. At the homogeneous coupling (J2 = J1) and its close neighborhood, the (canted) RPS state, established from an-harmonic fluctuations, lasts for low fields, Γ/J1 0.3, which is followed by a transition to the quantum paramagnet (polarized) phase at high fields. The transition from RPS state to the Néel phase is either a deconfined quantum phase transition or a first order one, however a continuous transition occurs between RPS and collinear phases.
International Journal of Modern Physics B, 1998
A simple modification of the standard Renormalization Group (RG) technique for the study of quant... more A simple modification of the standard Renormalization Group (RG) technique for the study of quantum spin systems is introduced. Our method which takes into account the effect of boundary conditions by employing the concept of superblock, may be regarded as a simple way for obtaining first estimates of many properties of spin systems. By applying this method to the XXZ spin-[Formula: see text] Heisenberg chain, we obtain the ground state energy with much higher accuracy than the standard RG. We have also obtained the staggered magnetization and the z-component of spin–spin correlation function which confirms the absence of long-range order in the massless region of the 1D XXZ model.
The European Physical Journal B, 2014
We study the thermal transport of a spin-1/2 two leg antiferromagnetic ladder in the direction of... more We study the thermal transport of a spin-1/2 two leg antiferromagnetic ladder in the direction of legs. The possible effect of spin-orbit coupling and crystalline electric field are investigated in terms of anisotropies in the Heisenberg interactions on both leg and rung couplings. The original spin ladder is mapped to a bosonic model via a bond-operator transformation where an infinite hard-core repulsion is imposed to constrain one boson occupation per site. The Green's function approach is applied to obtain the energy spectrum of quasi-particle excitations responsible for thermal transport. The thermal conductivity is found to be monotonically decreasing with temperature due to increased scattering among triplet excitations at higher temperatures. A tiny dependence of thermal transport on the anisotropy in the leg direction at low temperatures is observed in contrast to the strong one on the anisotropy along the rung direction, due to the direct effect of the triplet density. Our results reach asymptotically the ballistic regime of the spin-1/2 Heisenberg chain and compare favorably well with exact diagonalization data.
Physics Letters A, 1997
Inspired by the superblock method of White, we introduce a simple modification of the standard Re... more Inspired by the superblock method of White, we introduce a simple modification of the standard Renormalization Group (RG) technique for the study of quantum lattice systems. Our method which takes into account the effect of Boundary Conditions(BC), may be regarded as a simple way for obtaining first estimates of many properties of quantum lattice systems. By applying this method to the 1-dimensional free and interacting fermion system, we obtain the ground state energy with much higher accuracy than the standard RG. We also calculate the density-density correlation function in the free-fermion case which shows good agreement with the exact result.
Physical Review B, 2009
We have studied the two-dimensional anisotropic Kondo necklace model with antiferromagnetic ͑AF͒ ... more We have studied the two-dimensional anisotropic Kondo necklace model with antiferromagnetic ͑AF͒ Kondo coupling J Ќ and exchange coupling between "itinerant" spins J on the square lattice. The bond operator formalism is used to transform the spin model to a hard-core bosonic gas. We have used the Green's function approach to obtain the temperature dependence of spin excitation spectrum ͑triplet gap͒. We have also found the temperature dependence of the specific heat and the local spin-correlation function between localized and itinerant spins for various Kondo couplings J Ќ / J and anisotropies in both coupling strengths. Furthermore we studied the temperature dependence of the structure factor for localized spins which is determined by effective interactions via itinerant spins. For low temperature and close to the quantum critical point we have obtained an analytical formula for temperature dependence of the energy gap and specific heat. Finally we compared our results with those of previous mean-field treatments.
Physical Review B, 2004
We have generalized the application of cumulant expansion to ferrimagnetic systems of large spins... more We have generalized the application of cumulant expansion to ferrimagnetic systems of large spins. We have derived the effective Hamiltonian in terms of classical variables for a quantum ferrimagnet of large spins. A noninteracting gas of ferrimagnetic molecules is studied systematically by cumulant expansion to second order of (Js/T) where J is the exchange coupling in each molecule, s is the smaller spin (S1, s2) and T is temperature. We have observed fairly good results in the convergent regime of the expansion, i.e T > Js. We then extend our approach to a system of interacting ferrimagnetic molecules. For one dimensional nearest neighbor interaction we have observed that the correlation of more than two neighboring sites is negligible at moderate and high temperature behavior. Thus the results of a single molecule can be applied to the chain of interacting molecules for temperatures greater than classical energy scale, i.e T > JS1s2. Finally we will discuss the effect of spin inhomogeneity on the accuracy of this method.
Physical Review B, 2021
Magnons and phonons are two fundamental neutral excitations of magnetically ordered materials whi... more Magnons and phonons are two fundamental neutral excitations of magnetically ordered materials which can significantly dominate the low-energy thermal properties. In this work we study the interplay of magnons and phonons in honeycomb and Kagome lattices. When the mirror reflection with respect to the magnetic ordering direction is broken, the symmetry-allowed in-plane Dzyaloshinskii-Moriya (DM) interaction will couple the magnons to the phonons and the magnon-polaron states are formed. Besides, both lattice structures also allow for an out-of-plane DM interaction rendering the uncoupled magnons to be topological. Our aim is to study the interplay of such topological magnons with phonons. We show that the hybridization between magnons and phonons can significantly redistribute the Berry curvature among the bands. Especially, we found that the topological magnon band becomes trivial while the hybridized states at lower energy acquire Berry curvature strongly peaked near the avoided crossings. As such the thermal Hall conductivity of topological magnons shows significant changes due to coupling to the phonons.
Physical Review B, 2019
We investigate the ground-state phase diagram of the frustrated transverse field Ising (TFI) mode... more We investigate the ground-state phase diagram of the frustrated transverse field Ising (TFI) model on the checkerboard lattice (CL), which consists of Néel, collinear, quantum paramagnet and plaquette-valence bond solid (VBS) phases. We implement a numerical simulation that is based on the recently developed unconstrained tree tensor network (TTN) ansatz, which systematically improves the accuracy over the conventional methods as it exploits the internal gauge selections. At the highly frustrated region (J2 = J1), we observe a second order phase transition from plaquette-VBS state to paramagnet phase at the critical magnetic field, Γc = 0.28, with the associated critical exponents ν = 1 and γ ≃ 0.4, which are obtained within the finite size scaling analysis on different lattice sizes N = 4 × 4, 6 × 6, 8 × 8. The stability of plaquette-VBS phase at low magnetic fields is examined by spin-spin correlation function, which verifies the presence of plaquette-VBS at J2 = J1 and rules out the existence of a Néel phase. In addition, our numerical results suggest that the transition from Néel (for J2 < J1) to plaquette-VBS phase is a deconfined phase transition. Moreover, we introduce a mapping, which renders the low-energy effective theory of TFI on CL to be the same model on J1 − J2 square lattice (SL). We show that the plaquette-VBS phase of the highly frustrated point J2 = J1 on CL is mapped to the emergent string-VBS phase on SL at J2 = 0.5J1.
Physical Review B, 2016
We investigate the ground state nature of the transverse field Ising model on the J1 − J2 square ... more We investigate the ground state nature of the transverse field Ising model on the J1 − J2 square lattice at the highly frustrated point J2/J1 = 0.5. At zero field, the model has an exponentially large degenerate classical ground state, which can be affected by quantum fluctuations for non-zero field toward a unique quantum ground state. We consider two types of quantum fluctuations, harmonic ones by using linear spin wave theory (LSWT) with single-spin flip excitations above a long range magnetically ordered background and anharmonic fluctuations, by employing a cluster-operator approach (COA) with multi-spin cluster type fluctuations above a non-magnetic cluster ordered background. Our findings reveal that the harmonic fluctuations of LSWT fail to lift the extensive degeneracy as well as signaling a violation of the Hellmann-Feynman theorem. However, the stringtype anharmonic fluctuations of COA are able to lift the degeneracy toward a string-valence bond solid (VBS) state, which is obtained from an effective theory consistent with the Hellmann-Feynman theorem as well. Our results are further confirmed by implementing numerical tree tensor network simulation. The emergent non-magnetic string-VBS phase is gapped and breaks lattice rotational symmetry with only twofold degeneracy, which bears a continuous quantum phase transition at Γ/J1 ∼ = 0.50 to the quantum paramagnet phase of high fields. The critical behavior is characterized by ν ∼ = 1.0 and γ ∼ = 0.33 exponents.
Journal of the Physical Society of Japan, 2017
We develop the real space quantum renormalization group (QRG) approach for majorana fermions. As ... more We develop the real space quantum renormalization group (QRG) approach for majorana fermions. As an example we focus on the Kitaev chain to investigate the topological quantum phase transition (TQPT) in the one-dimensional spinless p-wave superconductor. Studying the behaviour of local compressibility and ground-state fidelity, show that the TQPT is signalled by the maximum of local compressibility at the quantum critical point tuned by the chemical potential. Moreover, a sudden drop of the ground-state fidelity and the divergence of fidelity susceptibility at the topological quantum critical point are used as proper indicators for the TQPT, which signals the appearance of Majorana fermions. Finally, we present the scaling analysis of ground-state fidelity near the critical point that manifests the universal information about the TQPT, which reveals two different scaling behaviors as we approach the critical point and thermodynamic limit.
The European Physical Journal B, 2015
We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ) on the an... more We study the effect of quantum fluctuations by means of a transverse magnetic field (Γ) on the antiferromagnetic J1 − J2 Ising model on the checkerboard lattice, the two dimensional version of the pyrochlore lattice. The zero-temperature phase diagram of the model has been obtained by employing a plaquette operator approach (POA). The plaquette operator formalism bosonizes the model, in which a single boson is associated to each eigenstate of a plaquette and the inter-plaquette interactions define an effective Hamiltonian. The excitations of a plaquette would represent an-harmonic fluctuations of the model, which lead not only to lower the excitation energy compared with a single-spin flip but also to lift the extensive degeneracy in favor of a plaquette ordered solid (RPS) state, which breaks lattice translational symmetry, in addition to a unique collinear phase for J2 > J1. The bosonic excitation gap vanishes at the critical points to the Néel (J2 < J1) and collinear (J2 > J1) ordered phases, which defines the critical phase boundaries. At the homogeneous coupling (J2 = J1) and its close neighborhood, the (canted) RPS state, established from an-harmonic fluctuations, lasts for low fields, Γ/J1 0.3, which is followed by a transition to the quantum paramagnet (polarized) phase at high fields. The transition from RPS state to the Néel phase is either a deconfined quantum phase transition or a first order one, however a continuous transition occurs between RPS and collinear phases.
Journal of physics. Condensed matter : an Institute of Physics journal, Jan 22, 2015
The Kondo-necklace model can describe magnetic low-energy limit of strongly correlated heavy ferm... more The Kondo-necklace model can describe magnetic low-energy limit of strongly correlated heavy fermion materials. There exist multiple energy scales in this model corresponding to each phase of the system. Here, we study quantum phase transition between the Kondo-singlet phase and the antiferromagnetic long-range ordered phase, and show the effect of anisotropies in terms of quantum information properties and vanishing energy gap. We employ the 'perturbative continuous unitary transformations' approach to calculate the energy gap and spin-spin correlations for the model in the thermodynamic limit of one, two, and three spatial dimensions as well as for spin ladders. In particular, we show that the method, although being perturbative, can predict the expected quantum critical point, where the gap of low-energy spectrum vanishes, which is in good agreement with results of other numerical and Green's function analyses. In addition, we employ concurrence, a bipartite entanglem...
Physical Review B, 2015
We study the interplay between the Kitaev and Ising interactions on both ladder and two dimension... more We study the interplay between the Kitaev and Ising interactions on both ladder and two dimensional lattices. We show that the ground state of the Kitaev ladder is a symmetry-protected topological (SPT) phase, which is protected by a Z2 × Z2 symmetry. It is confirmed by the degeneracy of the entanglement spectrum and non-trivial phase factors (inequivalent projective representations of the symmetries), which are obtained within infinite matrix-product representation of numerical density matrix renormalization group. We derive the effective theory to describe the topological phase transition on both ladder and two-dimensional lattices, which is given by the transverse field Ising model with/without next-nearest neighbor coupling based on the primary Ising configurations. The ladder has three phases, namely, the Kitaev SPT, symmetry broken ferro/antiferromagnetic order and classical spin-liquid. The non-zero quantum critical point and its corresponding central charge are provided by the effective theory, which are in full agreement with the numerical results, i.e., the divergence of entanglement entropy at the critical point, change of the entanglement spectrum degeneracy and a drop in the ground-state fidelity. The central charge of the critical points are either c=1 or c=2, with the magnetization and correlation exponents being 1/4 and 1/2, respectively. The transition from the classical spin-liquid phase of the frustrated Ising ladder to the Kitaev SPT phase is mediated by a floating phase, which shows strong finite entanglement scaling. In the absence of frustration, the 2D lattice shows a topological phase transition from the Z2 spin-liquid state to the long-range ordered Ising phase at finite ratio of couplings, while in the presence of frustration, an order-by-disorder transition is induced by the Kitaev term. The 2D classical spin-liquid phase is unstable against the addition of Kitaev term toward an ordered phase before the transition to the Z2 spin-liquid state.
Progress of Theoretical Physics, 2012
The exact factorized ground state of a heterogeneous (ferrimagnetic) spin model which is composed... more The exact factorized ground state of a heterogeneous (ferrimagnetic) spin model which is composed of two spins (ρ, σ) has been presented in detail. The Hamiltonian is not necessarily translational invariant and the exchange couplings can be competing antiferromagnetic and ferromagnetic arbitrarily between different sublattices to build many practical models such as dimerized and tetramerized materials and ladder compounds. The condition to get a factorized ground state is investigated for non-frustrated spin models in the presence of a uniform and a staggered magnetic field. According to the lattice model structure we have categorized the spin models in two different classes and obtained their factorization conditions. The first class contains models in which their lattice structures do not provide a single uniform magnetic field to suppress the quantum correlations. Some of these models may have a factorized ground state in the presence of a uniform and a staggered magnetic field. However, in the second class there are several spin models in which their ground state could be factorized whether a staggered field is applied to the system or not. For the latter case, in the absence of a staggered field the factorizing uniform field is unique. However, the degrees of freedom for obtaining the factorization conditions are increased by adding a staggered magnetic field.
Physical Review B, 2006
We have implemented three approaches to describe the thermodynamic properties of ferrimagnetic (S... more We have implemented three approaches to describe the thermodynamic properties of ferrimagnetic (S = 5/2, s = 2) spin chains. The application of cumulant expansion has been generalized to the ferrimagnetic chain in the presence of an external magnetic field. Using cumulants, we have obtained the field dependent effective Hamiltonian in terms of the classical variables up to the second order of quantum corrections. Thermodynamic functions, the internal energy, the specific heat and the magnetic susceptibility are obtained from the effective Hamiltonian. We have also examined the modified spin wave theory to derive the same physical properties. Finally, we have studied our model using quantum Monte Carlo simulation to obtain accurate results. The comparison of the above results and also the high temperature series expansion shows that cumulant expansion gives good results for moderate and high temperature regions while the modified spin wave theory is good for low temperatures. Moreover, the convergence regions of the cumulant expansion and the modified spin wave theory overlap each other which propose these two as a set of complement methods to get the thermodynamic properties of spin models.
Physical Review B, 2007
We have studied the phase diagram of the one dimensional S = 1 2 XXZ model with ferromagnetic nea... more We have studied the phase diagram of the one dimensional S = 1 2 XXZ model with ferromagnetic nearest-neighbor and antiferromagnetic next-nearest neighbor interactions. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points and the running of coupling constants. The second order QRG has been implemented to get the self similar Hamiltonian. This model shows a rich phase diagram which consists of different phases which possess the quantum spin-fluid and dimer phases in addition to the classical Néel and ferromagnetic ones. The border between different phases has been shown as a projection onto two different planes in the phase space.
Physical Review B, 2008
We have studied the phase diagram and entanglement of the one dimensional Ising model with Dzyalo... more We have studied the phase diagram and entanglement of the one dimensional Ising model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points, critical point and the scaling of coupling constants. This model has two phases, antiferromagnetic and saturated chiral ones. We have shown that the staggered magnetization is the order parameter of the system and DM interaction produces the chiral order in both phases. We have also implemented the exact diagonalization (Lanczos) method to calculate the static structure factors. The divergence of structure factor at the ordering momentum as the size of systems goes to infinity defines the critical point of the model. Moreover, we have analyzed the relevance of the entanglement in the model which allows us to shed insight on how the critical point is touched as the size of the system becomes large. Nonanalytic behavior of entanglement and finite size scaling have been analyzed which is tightly connected to the critical properties of the model. It is also suggested that a spin-fluid phase has a chiral order in terms of new spin operators which are defined by a nonlocal transformation.
Physical Review B, 2010
We have found the exact (factorized) ground state of a general class of ferrimagnets in the prese... more We have found the exact (factorized) ground state of a general class of ferrimagnets in the presence of a magnetic field which includes the frustrated, anisotropic and long range interactions for arbitrary dimensional space. In particular cases, our model represents the bond-alternating, ferromagnetantiferromagnet and also homogenous spin s model. The factorized ground state is a product of single particle kets on a bipartite lattice composed of two different spins (ρ, σ) which is characterized by two angles, a bi-angle state. The spin waves analysis around the exact ground state show two branch of excitations which is the origin of two dynamics of the model. The signature of these dynamics is addressed as a peak and a broaden bump in the specific heat.
Physical Review B, 2012
The expected phenomenology of non-interacting topological band insulators (TBI) is now largely th... more The expected phenomenology of non-interacting topological band insulators (TBI) is now largely theoretically understood. However, the fate of TBIs in the presence of interactions remains an active area of research with novel, interaction-driven topological states possible, as well as new exotic magnetic states. In this work we study the magnetic phases of an exchange Hamiltonian arising in the strong interaction limit of a Hubbard model on the honeycomb lattice whose noninteracting limit is a two-dimensional TBI recently proposed for the layered heavy transition metal oxide compound, (Li,Na)2IrO3. By a combination of analytical methods and exact diagonalization studies on finite size clusters, we map out the magnetic phase diagram of the model. We find that strong spin-orbit coupling can lead to a phase transition from an antiferromagnetic Neél state to a spiral or stripy ordered state. We also discuss the conditions under which a quantum spin liquid may appear in our model, and we compare our results with the different but related Kitaev-Heisenberg-J2-J3 model which has recently been studied in a similar context.
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Papers by Abdollah Langari