Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm

TL;DR

This paper introduces a novel tensor-network and kernel polynomial method to efficiently compute the spectrum and dynamics of open quantum many-body systems governed by the Liouvillian superoperator.

Contribution

The authors develop a non-Hermitian tensor-network kernel polynomial algorithm for solving the many-body Liouvillian spectrum and dynamics, enabling analysis beyond exact solutions.

Findings

Successfully computed the dephasing quantum compass model dynamics

Characterized quantum Zeno crossover and Stark localization effects

Explored the impact of many-body interactions on Liouvillian dynamics

Abstract

Understanding the dynamics of open quantum many-body systems is a major problem in quantum matter. Specifically, efficiently solving the spectrum of the Liouvillian superoperator governing such dynamics remains a critical open challenge. Here, we put forward a method for solving the many-body Liouvillian spectrum and dynamics based on the non-Hermitian kernel polynomial method and tensor-network techniques. We demonstrate the faithfulness of our method by computing the dynamics of the dephasing quantum compass model with a gradient magnetic field and comparing it with exact results. In particular, we show that our method allows us to characterize the quantum Zeno crossover and the reduction of relaxation rate due to Stark localization in this model. We further demonstrate the ability of our method to go beyond exact results by exploring nearest-neighbor interaction effects on the Liouvillian dynamics, elucidating the interplay between Stark localization and many-body interactions. Our method provides an efficient solution to many-body Liouvillian spectrum and dynamics, establishing a methodology to explore large open quantum many-body systems.