Assessment of spectral phases of non-Hermitian quantum systems through complex and singular values

Fuente: arXiv
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Main Authors: Prasad, Mahaveer, Tekur, S. Harshini, Agarwalla, Bijay Kumar, Kulkarni, Manas
Format: Preprint
Published: 2025
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author Prasad, Mahaveer
Tekur, S. Harshini
Agarwalla, Bijay Kumar
Kulkarni, Manas
author_facet Prasad, Mahaveer
Tekur, S. Harshini
Agarwalla, Bijay Kumar
Kulkarni, Manas
contents Chaotic behavior or lack thereof in non-Hermitian systems is often diagnosed via spectral analysis of associated complex eigenvalues. Very recently, singular values of the associated non-Hermitian systems have been proposed as an effective measure to study dissipative quantum chaos. Motivated by the rich properties of non-Hermitian power-law banded random matrices and its promise as a platform to study localized and delocalized phases in non-Hermitian systems, we make an in-depth study to assess different spectral phases of these matrices through the lens of both complex eigenvalues and singular values. Remarkably, the results from complex spectra and singular value analysis are seemingly different, thereby necessitating caution while identifying different phases. We also exemplify our findings by studying a non-Hermitian Hamiltonian with a complex on-site disorder. Our work indicates that systems, where disorder is present both in the Hermitian and non-Hermitian segments of a Hamiltonian, are sensitive to the specific diagnostic tool that needs to be employed to study quantum chaos.
format Preprint
id arxiv_https___arxiv_org_abs_2503_13387
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Assessment of spectral phases of non-Hermitian quantum systems through complex and singular values
Prasad, Mahaveer
Tekur, S. Harshini
Agarwalla, Bijay Kumar
Kulkarni, Manas
Statistical Mechanics
Disordered Systems and Neural Networks
Chaotic Dynamics
Chaotic behavior or lack thereof in non-Hermitian systems is often diagnosed via spectral analysis of associated complex eigenvalues. Very recently, singular values of the associated non-Hermitian systems have been proposed as an effective measure to study dissipative quantum chaos. Motivated by the rich properties of non-Hermitian power-law banded random matrices and its promise as a platform to study localized and delocalized phases in non-Hermitian systems, we make an in-depth study to assess different spectral phases of these matrices through the lens of both complex eigenvalues and singular values. Remarkably, the results from complex spectra and singular value analysis are seemingly different, thereby necessitating caution while identifying different phases. We also exemplify our findings by studying a non-Hermitian Hamiltonian with a complex on-site disorder. Our work indicates that systems, where disorder is present both in the Hermitian and non-Hermitian segments of a Hamiltonian, are sensitive to the specific diagnostic tool that needs to be employed to study quantum chaos.
title Assessment of spectral phases of non-Hermitian quantum systems through complex and singular values
topic Statistical Mechanics
Disordered Systems and Neural Networks
Chaotic Dynamics
url https://arxiv.org/abs/2503.13387