Realizing Constrained Wishart-Laguerre Ensembles in Disordered Spin Chains: A Random Matrix Approach

We numerically realize the real and complex fixed-trace Wishart-Laguerre ensembles (FTWL) of random density matrices, demonstrating a crossover between these two prominent random matrix ensembles in a disordered, correlated spin chain model using several short- and long-range spectral correlation measures such as spectral density, extreme Schmidt eigenvalue distributions and the entanglement spectral form factor of these Schmidt eigenvalues. The spin chain includes standard Ising and Heisenberg interactions, combined with a random transverse field and a scalar spin-chirality term [1] leading to both conventional and unconventional time-reversal symmetry breaking leading to this crossover, that has remained largely unexplored in the context of random matrices. We further investigate the recently introduced singular value decomposition entanglement entropy [2] for the eigenstates of the energy and entanglement spectra of this spin chain, comparing it with the commonly used average von Neumann entropy to further analyze this symmetry class crossover from a quantum information-theoretic perspective.

[1] Spectral crossovers and universality in quantum spin chains coupled to random fields, D. Kundu, S. Kumar, and S. S Gupta, Phys. Rev. B 105, 014205 (2022)

[2] SVD Entanglement Entropy, A. J. Parzygnat, T. Takayanagi, Y. Taki & Z. Wei, JHEP 12 (2023) 123 (2024).