Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI^† and AII^†

2024/10/31 by Kulkarni, Anish, Kawabata, Kohei, Ryu, Shinsei · 1 citation
#Chaotic Dynamics (nlin.CD) #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2410.24043

Abstract

Symmetry of non-Hermitian matrices underpins many physical phenomena. In particular, chaotic open quantum systems exhibit universal bulk spectral correlations classified on the basis of time-reversal symmetry^† (TRS^†), coinciding with those of non-Hermitian random matrices in the same symmetry class. Here, we analytically study the spectral correlations of non-Hermitian random matrices in the presence of TRS^† with signs +1 and -1, corresponding to symmetry classes AI^† and AII^†, respectively. Using the fermionic replica non-linear sigma model approach, we derive n-fold integral expressions for the nth moment of the one-point and two-point characteristic polynomials. Performing the replica limit n→ 0, we qualitatively reproduce the density of states and level-level correlations of non-Hermitian random matrices with TRS^†.

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• Spectral Density and Eigenvector Nonorthogonality in Complex Symmetric Random Matrices

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