Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm

TL;DR

This paper introduces a novel algorithm combining superoperator renormalization and TEBD techniques to efficiently simulate mixed-state dynamics in one-dimensional quantum lattice systems, including thermal states and master equation evolutions.

Contribution

The paper develops a new algorithm that efficiently simulates mixed-state dynamics in 1D quantum systems using superoperator renormalization and TEBD, enabling studies of thermal states and real-time evolution.

Findings

Algorithm efficiently describes system states with linear system size dependence.

Simulations successfully performed on quantum spins and fermions in 1D.

Computational cost scales with correlations, not system size.

Abstract

We present an algorithm to study mixed-state dynamics in one-dimensional quantum lattice systems. The algorithm can be used, e.g., to construct thermal states or to simulate real time evolutions given by a generic master equation. Its two main ingredients are (i) a superoperator renormalization scheme to efficiently describe the state of the system and (ii) the time evolving block decimation (TEBD) technique to efficiently update the state during a time evolution. The computational cost of a simulation increases significantly with the amount of correlations between subsystems but it otherwise depends only linearly in the system size. We present simulations involving quantum spins and fermions in one spatial dimension.