A matrix product operator approach to non-equilibrium Floquet steady states

TL;DR

This paper introduces OFDMRG, a matrix product operator method for simulating non-equilibrium Floquet steady states in open quantum systems, enabling large-scale analysis beyond traditional techniques.

Contribution

The paper develops a novel numerical approach using matrix product operators for Floquet density matrices, allowing efficient simulation of large dissipative driven systems.

Findings

Successfully benchmarks the method with a driven-dissipative Ising model.

Demonstrates potential for stabilizing time-crystalline order via dissipation.

Enables studying long-time dynamics in open Floquet systems.

Abstract

We present a numerical method to simulate non-equilibrium Floquet steady states of one-dimensional periodically-driven (Floquet) many-body systems coupled to a dissipative bath, called open-system Floquet DMRG (OFDMRG). This method is based on a matrix product operator ansatz for the Floquet density matrix in frequency-space, and enables access to large systems beyond the reach of exact master-equation or quantum trajectory simulations, while retaining information about the periodic micro-motion in Floquet steady states. An excited-state extension of this technique also allows computation of the dynamical approach to the steady state on asymptotically long timescales. We benchmark the OFDMRG approach with a driven-dissipative Ising model, and apply it to study the possibility of dissipatively stabilizing pre-thermal discrete time-crystalline order by coupling to a cold bath.