Relaxation of a one-dimensional Mott insulator after an interaction quench

Abstract

We obtain the exact time evolution for the one-dimensional integrable fermionic 1/r Hubbard model after a sudden change of its interaction parameter, starting from either a metallic or a Mottinsulating eigenstate. In all cases the system relaxes to a new steady state, showing that the presence of the Mott gap does not inhibit relaxation. The properties of the final state are described by a generalized Gibbs ensemble. We discuss under which conditions such ensembles provide the correct statistical description of isolated integrable systems in general. We find that generalized Gibbs ensembles do predict the properties of the steady state correctly, provided that the observables or initial states are sufficiently uncorrelated in terms of the constants of motion.

Equilibration and prethermalization in the Bose-Hubbard and Fermi-Hubbard models

“…7 can be compared with the results of Ref. [50] where the (integrable) Fermi-Hubbard model in one dimension with long-range hopping (i.e., T µν contributes not just for nearest neighbors) is considered and we observe qualitative agreement (see, e.g., Fig. 1d in Ref.…”

“…1d in Ref. [50]). Unfortunately, a quantitative comparison of our results for the higher-dimensional Fermi-Hubbard model is impeded by the lack of data for the regime under consideration in our present work.…”

“…For fermions in one spatial dimension, the integrability of the Fermi-Hubbard model facilitates the derivation of the exact evolution after a quench including effects such as "pre-thermalization" [13,50,51]. Again, in higher dimensions, appropriate approximations are necessary, such as a time-dependent Monte-Carlo method [52], time-dependent dynamical mean field theory [53][54][55][56][57], the Gutzwiller ansatz for fermions [58][59][60], the flow equation method [9,10,61,62], or effective quasi-particle methods [63].…”

Quantum quench dynamics of the Coulomb Luttinger model

“…Even in the more traditional condensed matter systems, the Coulomb interaction between electrons is very often screened, particularly in non-isolated 1D systems 30 , giving rise to an effective short-range interaction description in most of the cases. However, this does not exhaust the possibilities of studying out of equilibrium systems, and in particular the consequences of a long-range potential seems to be unexplored, though some results are available in a Hubbard chain with long-range hopping 31 . A concrete realization of particles interacting via a long-range potential are linear ion traps 32 .…”

Long time dynamics following a quench in an integrable quantum spin chain: Local versus nonlocal operators and effective thermal behavior

“…This understanding was distilled into the proposal of a generalized Gibbs ensemble, keeping track of the initial value of all the constants of motion 18 and constructed to describe the steady state reached after a quench. Several works have tested the conditions of applicability of such Gibbs distribution and its drawbacks [16][17][18]21,[28][29][30]34 . In particular, for a special quench in a 1D Bose-Hubbard model 26 , for integrable systems with free quasiparticles 27 and for the computation of one-point correlation functions for a specific class of quench processes in otherwise generic integrable systems 21 , the long-time limit of the dynamics was shown to be well described by the generalized Gibbs ensemble.…”