Power-law random banded matrix ensemble as the effective model for many-body localization transition
School of Science, Hangzhou Dianzi University, 310027, Hangzhou, China
Accepted: 19 March 2022
Published online: 29 March 2022
We employ the power-law random banded matrix (PRBM) ensemble with single tuning parameter as the effective model for many-body localization (MBL) transition in random spin systems. We show the PRBM accurately reproduces the eigenvalue statistics on the entire phase diagram through the fittings of high-order spacing ratio distributions as well as number variance , 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 , close to the value obtained in 1D physical model by exact diagonalization, while the computational cost here is much less.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022