Edwards polaron formation : From one to three dimensions

arXiv (Cornell University), 2024

We investigate the transport properties of massive Dirac fermions subjected to uncorrelated scalar potential disorder, and mass disorder. Using a finite difference method, the conductance is calculated for a wide variety of combinations of these two disorder strengths. By calculating the scaling of conductivity with system size we find that, depending on the combination, the system can have an insulating, scale invariant, and metallic behavior. We identify the critical values of these disorder strengths where the phase transitions occur. We study both the zero and nonzero average mass cases to examine the effect of scalar potential disorder on band gap. Our results suggest a suppression of the band gap by the scalar potential disorder.

physica status solidi (b), 2019

The transport of strongly correlated bosons in a three‐dimensional optical lattice is studied within the Bose–Hubbard approximation. The transport is induced by a small displacement of the overall harmonic trapping potential. The subsequent relaxation dynamics is monitored by high precision density measurements with the help of scanning electron microscopy. Good agreement with a real space time‐dependent Gutzwiller mean‐field description is found.

Physical Review B, 2003

The main features of a generic boson-fermion scenario for electron pairing in a many-body correlated fermionic system are: i) a cross-over from a poor metal to an insulator and finally a superconductor as the temperature decreases, ii) the build-up of a finite amplitude of local electron pairing below a certain temperature T * , followed by the onset of long-range phase correlations among electron pairs below a second characteristic temperature T φ , iii) the opening of a pseudogap in the DOS of the electrons below T * , rendering these electrons poorer and poorer quasi-particles as the temperature decreases, with the electron transport becoming ensured by electron pairs rather than by individual electrons. A number of these features have been so far obtained on the basis of different many-body techniques, all of which have their built-in shortcomings in the intermediate coupling regime, which is of interest here. In order to substantiate these features, we investigate them on the basis of an exact diagonalization study on rings up to eight sites. Particular emphasis has been put on the possibility of having persistent currents in mesoscopic rings tracking the change-over from single-to two-particle transport as the temperature decreases and the superconducting state is approached.

arXiv: Quantum Physics, 2020

We study the strong coupling dynamics as well as transport properties of photons in the two-bath spin-boson model, in which a spin-1/2 particle is frustratingly coupled to two independent Ohmic bosonic baths. Using a combination of numerical and analytical methods, we show that the frustration in this model gives rise to rich physics in a very wide range of energies. This is in contrast to the one-bath spin-boson model, where the non-trivial physics occurs at an energy scale close to the renormalized spin frequency. The renormalized spin frequency in the two-bath spin-boson model is still important, featuring in different observables, including the non-equiblirum dynamics of both the spin and the baths along with the elastic transport properties of a photon. The latter however reveals a much more complex structure. The elastic scattering displays non-monotonic behavior at high frequencies, and is very different in the two channels: intra- and inter-bath scattering. The photon can al...

The European Physical Journal B- …, 1999

We investigate polaron formation in a many-electron system in the presence of a local repulsion sufficiently strong to prevent local-bipolaron formation. Specifically, we consider a Hubbard-Holstein model of interacting electrons coupled to dispersionless phonons of frequency ω0. Numerically solving the model in a small one-dimensional cluster, we find that in the nearly adiabatic case ω0 < t, the necessary and sufficient condition for the polaronic regime to occur is that the energy gain in the atomic (i.e., extremely localized) regime E pol overcomes the energy of the purely electronic system E el . In the antiadiabatic case, ω0 > t, polaron formation is instead driven by the condition of a large ionic displacement g/ω0 > 1 (g being the electron-phonon coupling). Dynamical properties of the model in the weak and moderately strong coupling regimes are also analyzed.

Physical Review B, 2016

Quantum transport of strongly correlated fermions is of central interest in condensed matter physics. Here, we present first-principle nonequilibrium Green functions results using T-matrix selfenergies for finite Hubbard clusters of dimension 1, 2, 3. We compute the expansion dynamics following a potential quench and predict its dependence on the interaction strength and particle number. We discover a universal scaling, allowing an extrapolation to infinite-size systems, which shows excellent agreement with recent cold atom diffusion experiments [Schneider et al., Nat. Phys. 8, 213 (2012)].

Physical Review A, 2010

The ground-state phase diagram of mixtures of spin polarized fermions and bosons in a 1D periodic lattice is discussed in the limit of large fermion hopping and half filling of the fermions. Numerical simulations performed with the density matrix renormalization group (DMRG) show besides bosonic Mott insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a novel phase with spatial separation of MI and CDW regions. We derive an effective bosonic theory which allows for a complete understanding and quantitative prediction of the bosonic phase diagram. In particular the origin of CDW phase and the MI-CDW phase separation is revealed as the interplay between fermion-induced mean-field potential and long range interaction with alternating sign.

2009

The ground-state phase diagram of mixtures of spin polarized fermions and bosons in a 1D periodic lattice is discussed in the limit of large fermion hopping and half filling of the fermions. Numerical simulations performed with the density matrix renormalization group (DMRG) show besides bosonic Mott insulating (MI), superfluid (SF), and charge density-wave phases (CDW) a novel phase with spatial separation of MI and CDW regions. We derive an effective bosonic theory which allows for a complete understanding and quantitative prediction of the bosonic phase diagram. In particular the origin of CDW phase and the MI-CDW phase separation is revealed as the interplay between fermion-induced mean-field potential and long range interaction with alternating sign.

Journal of physics, 2000

We study transport in a class of exactly solvable models of interacting fermions in one dimension. We contrast these models with models of non-interacting fermions in an Aharanov-Bohm ring to which they are superficially similar. We introduce magnetic and non-magnetic impurities at a site, through either a weak δ-function potential or through a weak link. Using a renormalisation group analysis, we show that the strength of the nonmagnetic impurity is not affected by the interaction, whereas the magnetic impurity cuts the wire at the impurity site.

Physical Review D, 2009

We present numerical solutions of the semi-classical Boltzmann-Vlasov equation for fermion particle-antiparticle production by strong electric fields in boost-invariant coordinates in (1+1) and (3+1) dimensional QED. We compare the Boltzmann-Vlasov results with those of recent quantum field theory calculations and find good agreement. We conclude that extending the Boltzmann-Vlasov approach to the case of QCD should allow us to do a thorough investigation of how backreaction affects recent results on the dependence of the transverse momentum distribution of quarks and anti-quarks on a second Casimir invariant of color SU(3).

Physical Review B, 2011

The 2D lattice gas model with competing short and long range interactions is used for calculation of the incoherent charge transport in the classical strongly-correlated charge segregated polaronic state. We show, by means of Monte-Carlo simulations, that at high temperature the transport is dominated by hopping of the dissociated correlated polarons, where their mobility is inversely proportional to the temperature, µ ∝ T −1 . At temperatures below the clustering transition temperature the bipolaron transport becomes dominant. The energy barrier for the bipolaron hopping is determined by Coulomb effects and is found to be lower than the barrier for the single-polaron hopping. This leads to drastically different temperature dependencies of mobilities for polarons and bipolarons at low temperatures.

Physical Review B, 2012

We consider 2D Dirac fermions in the presence of three types of disorder: random scalar potential, random gauge potential and random mass with long-range correlations decaying as a power law. Using various methods such as the self-consistent Born approximation (SCBA), renormalization group (RG), the matrix Green function formalism and bosonisation we calculate the density of states and study the full counting statistics of fermionic transport at lower energy. The SCBA and RG show that the random correlated scalar potentials generate an algebraically small energy scale below which the density of states saturates to a constant value. For correlated random gauge potential, RG and bosonisation calculations provide consistent behavior of the density of states which diverges at zero energy in an integrable way. In the case of correlated random mass disorder the RG flow has a nontrivial infrared stable fixed point leading to a universal power-law behavior of the density of states and also to universal transport properties. In contrast to uncorrelated case the correlated scalar potential and random mass disorders give rise to deviation from the pseudodiffusive transport already to lowest order in disorder strength.

JOURNAL OF SUPERCONDUCTIVITY, 1999

We study the crossover to small polarons in the Holstein model for finitedensities in presence of strong electronic correlations. The small polaronformation condition ?&amp;amp;amp;gt;1, which holds for a single particle in theadiabatic regime ?0/t«1 is generalized to the many particle case bymeans of simple physical arguments. It is shown that a general criterion canbe formulated for polaron formation, provided that incoherent 1/?corrections are taken into account.

Physical Review B, 1997

A dynamical mean-field theory of the small polaron problem is presented, which becomes exact in the limit of infinite dimensions. The ground state properties and the one-electron spectral function are obtained for a single electron interacting with Einstein phonons by a mapping of the lattice problem onto a polaronic impurity model. The one-electron propagator of the impurity model is calculated through a continued fraction expansion (CFE), both at zero and finite temperature, for any electron-phonon coupling and phonon energy. In contrast to the ground state properties such as the effective polaron mass, which show a continuous behaviour as the coupling is increased, spectral properties exhibit a sharp qualitative change at low enough phonon frequency: beyond a critical coupling, one energy gap and then more and more open in the density of states at low energy, while the high energy part of the spectrum is broad and can be qualitatively explained by a strong coupling adiabatic approximation. As a consequence narrow and coherent low-energy subbands coexist with an incoherent featureless structure at high energy. The subbands denote the formation of quasiparticle polaron states. Also, divergencies of the self-energy may occur in the gaps. At finite temperature such effect triggers an important damping and broadening of the polaron subbands. On the other hand, in the large phonon frequency regime such a separation of energy scales does not exist and the spectrum has always a multipeaked structure.

Philosophical Magazine, 2013

We introduce a theoretical model to scrutinize the conductivity of small polarons in one-dimensional disordered systems, focusing on two crucial-as will be demonstrated-factors: the density of states and the spatial extent of the electronic wave function. The investigation is performed for any temperature up to 300 K and under electric field of arbitrary strength up to the polaron dissociation limit. To accomplish this task we combine analytical work with numerical calculations.