Nonequilibrium Quantum Dynamics of a Charge Carrier Doped into a Mott Insulator

Abstract

We study real-time dynamics of a charge carrier introduced into undoped Mott insulator propagating under a constant electric field F on the t-J ladder and square lattice. We calculate quasistationary current. In both systems adiabatic regime is observed followed by the positive differential resistivity (PDR) at moderate fields where carrier mobility is determined. Quantitative differences between ladder and 2-dimensional (2D) system emerge when at large fields both systems enter negative differential resistivity (NDR) regime. In the ladder system Bloch-like oscillations prevail, while in 2D the current remains finite, proportional to 1/F . The crossover between PDR and NDR regime in 2D is accompanied by a change of the spatial structure of the propagating spin polaron. [12,13] and the relaxation of correlated systems after the photoexcitations [14,15], represent the well-studied examples of nonequilibrium phenomena which are important both for fundamental understanding of strongly correlated systems as well as for their potential applications.Most of theoretical studies so far considered the breakdown of undoped MI, when threshold value of the electric field exceeds experimental value [9] by a few orders of magnitude (see discussion in Ref. [11]). It indicates that other transport mechanism becomes active at energies much lower than the Mott-Hubbard gap. In this Letter we inveqstigate a nonequilibrium response of a charge carrier doped into the insulator and driven by an uniform electric field F . Understanding of this subject on one hand widens our knowledge of a charge carrier doped into the antiferromagnetic (AFM) background [16,17], on the other, it represents a fundamental problem of a quantum particle moving in a dissipative medium [18].Having in mind strongly correlated systems, we investigate the t-J model where the particle driven by a constant electric field dissipates the energy by inelastic scattering on spin degrees of freedom. We use numerical approaches to treat t-J model at zero temperature on two different system geometries, i.e., a ladder with periodic boundary conditions and an infinite 2-dimensional (2D)

Two Holes in the t–J Model Form a Bound State for Any Nonzero J/t

“…The method has been successfully applied to calculation of the ground state of the t-J model with one [13,15] and two doped holes [11,14,16], as well as extended to studies of the t-J model with lattice degrees of freedom [14,17,18]. One of the significant advantages of the method represents its ability to study large hole distances up to N h + 1.…”

Approach to a stationary state in a driven Hubbard model coupled to a thermostat

“…To begin with, we plot in Fig. 4(a) the steady current J nss , which shows a linear/nonlinear crossover as a function of the electric field, as repeatedly reported in similar problems 29,30 . At small fields the current is linear in the field E, as expected by continuity with perturbed equilibrium state, then it reaches a maximum before decreasing as the field is further increased.…”

Nonequilibrium dynamical mean-field theory and its applications

“…Steady-state current in a dissipative system While Bloch oscillations are a typical transient phenomenon, a true stationary state with nonzero current in an interacting system can only be reached when the system is coupled to an external heat bath. [The bath might also be part of the model, as in the situation of a single carrier in a manybody background (Mierzejewski et al, 2011;Golež et al, 2013).] Otherwise, the Joule heating of the system leads to a time-dependent change in the total energy.…”