Related papers: A Krylov space approach to Singular Value Decomposition in non-Hermitian systems

A Krylov space approach to Singular Value Decomposition in non-Hermitian systems

URL: http://arxiv.org/abs/2411.09309v1
Date: Thu, 14 Nov 2024 09:37:45 GMT
Title: A Krylov space approach to Singular Value Decomposition in non-Hermitian systems
Authors: Pratik Nandy, Tanay Pathak, Zhuo-Yu Xian, Johanna Erdmenger,
Abstract summary: We propose a novel tridiagonalization approach for non-Hermitian random matrices and Hamiltonians. This technique leverages the real and non-negative nature of singular values, bypassing the complex eigenvalues typically found in non-Hermitian systems. We analytically compute the Krylov complexity for two-dimensional non-Hermitian random matrices within a subset of non-Hermitian symmetry classes.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We propose a novel tridiagonalization approach for non-Hermitian random matrices and Hamiltonians using singular value decomposition (SVD). This technique leverages the real and non-negative nature of singular values, bypassing the complex eigenvalues typically found in non-Hermitian systems. We analyze the tridiagonal elements, namely the Lanczos coefficients and the associated Krylov (spread) complexity, appropriately defined through the SVD, across several examples including Ginibre ensembles and the non-Hermitian Sachdev-Ye-Kitaev (SYK) model. We demonstrate that in chaotic cases, the complexity exhibits a distinct peak due to the repulsion between singular values, a feature absent in integrable cases. Using our approach, we analytically compute the Krylov complexity for two-dimensional non-Hermitian random matrices within a subset of non-Hermitian symmetry classes including time-reversal, time-reversal$^{\dagger}$, chiral, and sublattice symmetry.

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