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

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.

6 pages, 3 figures + supplemental material (6 pages, 5 figures)

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• Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm
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• $\mathcal{P}\mathcal{T}$-Symmetry breaking in quantum spin chains with exceptional non-Hermiticities
• Self-consistent tensor network method for correlated super-moiré matter beyond one billion sites
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• Probing phase transitions in non-Hermitian systems with quantum entanglement
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