Non-Unitary Quantum Many-Body Dynamics using the Faber Polynomial Method

TL;DR

This paper introduces a Faber polynomial-based numerical method to simulate non-unitary quantum many-body dynamics, effectively handling non-Hermitian systems, quantum jumps, and skin effects, with applications to the Hatano-Nelson model and quantum spin chains.

Contribution

It generalizes Chebyshev polynomial methods to non-Hermitian cases, enabling efficient simulation of complex non-unitary quantum dynamics and unraveling quantum jump processes.

Findings

Interactions preserve magnetic order against skin effect.

Numerical evidence of hydrodynamic behavior in domain-wall melting.

Analysis of skin effects in quantum spin chains.

Abstract

Efficient numerical methods are still lacking to probe the unconventional dynamics of quantum many-body systems under non-unitary evolution. In this work, we use Faber polynomials to numerically simulate both the dynamics of non-Hermitian systems and the quantum jumps unravelling of the Lindblad dynamics. We apply the method to the non-interacting and interacting Hatano-Nelson models evolving from two different setups: i) a N\'eel state, and ii) a domain wall. In the first case, we study how interactions preserve the initial magnetic order against the skin effect. In the second example, we present numerical evidence of the existence of an effective hydrodynamic description for the domain-wall melting problem in the non-interacting limit. Additionally, we investigate both the conditional and unconditional dynamics of the quantum jump unravelling in two quantum spin chains, which exhibit either the non-Hermitian or the Liouvillian skin effect. This numerical method inherently generalises the well-established method based on Chebyshev polynomials to accommodate non-Hermitian scenarios.