Steady States of Infinite-Size Dissipative Quantum Chains via Imaginary Time Evolution

TL;DR

This paper introduces a combined imaginary and real time tensor network approach to efficiently find nonequilibrium steady states of infinite dissipative quantum chains, demonstrated on the quantum Ising model.

Contribution

The method enables direct convergence to steady states in the thermodynamic limit by bypassing highly correlated states, improving accuracy and efficiency.

Findings

Successfully applied to the dissipative transverse field quantum Ising chain.

Confirmed the smooth crossover of the order parameter in the thermodynamic limit.

Demonstrated the method's ability to handle infinite-size quantum systems.

Abstract

Directly in the thermodynamic limit, we show how to combine imaginary and real time evolution of tensor networks to efficiently and accurately find the nonequilibrium steady states (NESS) of one-dimensional dissipative quantum lattices governed by the Lindblad master equation. The imaginary time evolution first bypasses any highly correlated portions of the real-time evolution trajectory by directly converging to the weakly correlated subspace of the NESS, after which real time evolution completes the convergence to the NESS with high accuracy. We demonstrate the power of the method with the dissipative transverse field quantum Ising chain. We show that a crossover of an order parameter shown to be smooth in previous finite-size studies remains smooth in the thermodynamic limit.