Field theory of non-Hermitian disordered systems

Fuente: arXiv
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Main Authors: Chen, Ze, Kawabata, Kohei, Kulkarni, Anish, Ryu, Shinsei
Format: Preprint
Published: 2024
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author Chen, Ze
Kawabata, Kohei
Kulkarni, Anish
Ryu, Shinsei
author_facet Chen, Ze
Kawabata, Kohei
Kulkarni, Anish
Ryu, Shinsei
contents The interplay between non-Hermiticity and disorder gives rise to unique universality classes of Anderson transitions. Here, we develop a field-theoretical description of non-Hermitian disordered systems based on fermionic replica nonlinear sigma models. We classify the target manifolds of the nonlinear sigma models across all the 38-fold symmetry classes of non-Hermitian systems and corroborate the correspondence of the universality classes of Anderson transitions between non-Hermitian systems and Hermitized systems with additional chiral symmetry. We apply the nonlinear sigma model framework to study the spectral properties of non-Hermitian random matrices with particle-hole symmetry. Furthermore, we demonstrate that the Anderson transition unique to nonreciprocal disordered systems in one dimension, including the Hatano-Nelson model, originates from the competition between the kinetic and topological terms in a one-dimensional nonlinear sigma model. We also discuss the critical phenomena of non-Hermitian disordered systems with symmetry and topology in higher dimensions.
format Preprint
id arxiv_https___arxiv_org_abs_2411_11878
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Field theory of non-Hermitian disordered systems
Chen, Ze
Kawabata, Kohei
Kulkarni, Anish
Ryu, Shinsei
Disordered Systems and Neural Networks
The interplay between non-Hermiticity and disorder gives rise to unique universality classes of Anderson transitions. Here, we develop a field-theoretical description of non-Hermitian disordered systems based on fermionic replica nonlinear sigma models. We classify the target manifolds of the nonlinear sigma models across all the 38-fold symmetry classes of non-Hermitian systems and corroborate the correspondence of the universality classes of Anderson transitions between non-Hermitian systems and Hermitized systems with additional chiral symmetry. We apply the nonlinear sigma model framework to study the spectral properties of non-Hermitian random matrices with particle-hole symmetry. Furthermore, we demonstrate that the Anderson transition unique to nonreciprocal disordered systems in one dimension, including the Hatano-Nelson model, originates from the competition between the kinetic and topological terms in a one-dimensional nonlinear sigma model. We also discuss the critical phenomena of non-Hermitian disordered systems with symmetry and topology in higher dimensions.
title Field theory of non-Hermitian disordered systems
topic Disordered Systems and Neural Networks
url https://arxiv.org/abs/2411.11878