Optimal time-dependent lattice models for nonequilibrium dynamics

TL;DR

This paper introduces a novel approach to constructing optimal time-dependent lattice models using time-dependent Wannier functions and the variational principle, enabling efficient simulation of nonequilibrium dynamics.

Contribution

It develops a new method for creating time-dependent lattice models that adapt to system dynamics, improving modeling accuracy for nonequilibrium quantum systems.

Findings

Identifies a separation of timescales in the dynamics.

Shows multi-band dynamics can be approximated by single-band models.

Demonstrates the method on the Bose-Hubbard model with time-dependent Wannier functions.

Abstract

Lattice models are abundant in theoretical and condensed-matter physics. Generally, lattice models contain time-independent hopping and interaction parameters that are derived from the Wannier functions of the noninteracting problem. Here, we present a new concept based on time-dependent Wannier functions and the variational principle that leads to optimal time-dependent lattice models. As an application, we use the Bose-Hubbard model with time-dependent Wannier functions to study a quench scenario involving higher bands. We find a separation of times scales in the dynamics and show that under some circumstances the multi-band nonequilibrium dynamics of a quantum system can be obtained essentially at the cost of a single-band model.