Topological spin excitations in non-Hermitian spin chains with a generalized kernel polynomial algorithm

TL;DR

This paper introduces a novel numerical method combining the kernel polynomial approach and tensor networks to compute spectral functions in non-Hermitian many-body systems, revealing topological spin excitations and handling the non-Hermitian skin effect.

Contribution

It develops an efficient algorithm for spectral function computation in non-Hermitian many-body models, capturing topological features and addressing the skin effect.

Findings

Reveals topological spin excitations in a non-Hermitian spin model

Accurately reflects non-trivial line gap topology in many-body systems

Effective even with the non-Hermitian skin effect

Abstract

Spectral functions of non-Hermitian Hamiltonians can reveal the existence of topologically non-trivial line gaps and the associated topological edge modes. However, the computation of spectral functions in a non-Hermitian many-body system remains an open challenge. Here, we put forward a numerical approach to compute spectral functions of a non-Hermitian many-body Hamiltonian based on the kernel polynomial method and the matrix-product state formalism. We show that the local spectral functions computed with our algorithm reveal topological spin excitations in a non-Hermitian spin model, faithfully reflecting the non-trivial line gap topology in a many-body model. We further show that the algorithm works in the presence of the non-Hermitian skin effect. Our method offers an efficient way to compute local spectral functions in non-Hermitian many-body systems with tensor-networks, allowing to characterize line gap topology in non-Hermitian quantum many-body models.