Power-Law Random Banded Matrix Ensemble as the Effective Model for Many-Body Localization Transition

Abstract

We employ the power-law random band matrix (PRBM) ensemble with single tuning parameter $\mu$ as the effective model for many-body localization (MBL) transition in random spin systems. We show the PRBM accurately reproduce the eigenvalue statistics on the entire phase diagram through the fittings of high-order spacing ratio distributions $P(r^{(n)})$ as well as number variance ${\Sigma }^2(l)$, in systems both with and without time-reversal symmetry. For the properties of eigenvectors, it's shown the entanglement entropy of PRBM displays an evolution from volume-law to area-law behavior which signatures an ergodic-MBL transition, and the critical exponent is found to be $\nu =0.83\pm 0.15$, close to the value obtained in 1D physical model by exact diagonalization while the computational cost here is much less.

8 pages, 6 figures

References in corpus (11)

• Anderson Transitions
• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Many body localization in Heisenberg XXZ magnet in a random field
• Many-Body Localization in a Quasiperiodic System
• Quantum quenches in the many-body localized phase
• Higher-order level spacings in random matrix theory based on Wigner's conjecture
• Scattering at the Anderson transition: Power--law banded random matrix model
• Critical Level Statistics at the Many-Body Localization Transition Region
• Random Matrix Model for Eigenvalue Statistics in Random Spin Systems

Cited by in corpus (4)

• Scattering and transport properties of the three classical Wigner-Dyson ensembles at the Anderson transition
• Complexity Measure Diagnostics of Ergodic to Many-Body Localization Transition
• Power-law banded random matrix ensemble as a model for quantum many-body Hamiltonians
• Quantum Markov chain Monte Carlo method with programmable quantum simulators