Fragment Percolating and Many Body Localization Transition

TL;DR

This paper introduces a novel percolation-based approach to analyze the many-body localization transition in disordered bosonic systems, providing estimates for the transition point and critical exponents.

Contribution

It proposes a new method using eigenvector fragmentation and percolation concepts to study the MBL transition, offering a different perspective from traditional techniques.

Findings

Transition point at W_c ≈ 12-13

Localization length exponent ν ≈ 2.0

Fragmentation method effectively locates the MBL transition

Abstract

Elements of eigenvectors obtained by exact diagonalization can be considered as two dimensional lattice sites, in which dynamics of a given initial state is seen as a percolating procedure on the lattice sites. Then one can use the percolating procedure to generate a series of fragments of eigenvectors. Combining the fraction ratio and entanglement entropy dynamics of the generated fragment we examine the many-body localization transition in a disordered hard-core bosonic model. It helps us to locate roughly the transition point at the critical disorder strength $W_c\approx 12\sim13$. The scaling collapse of the fraction ratios gives us the localization length exponent $\nu\approx2.0$.