Field theory of non-Hermitian disordered systems

Ze Chen; Kohei Kawabata; Anish Kulkarni; Shinsei Ryu

doi:10.1103/physrevb.111.054203

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arXiv · 2411.11878

Field theory of non-Hermitian disordered systems

Ze Chen·Kohei Kawabata·Anish Kulkarni·Shinsei Ryu

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Abstract

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.

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Ze Chen, Kohei Kawabata, Anish Kulkarni, Shinsei Ryu. 2024-11-04. Field theory of non-Hermitian disordered systems. https://doi.org/10.1103/physrevb.111.054203

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