Role of Fock-space correlations in many-body localization

Thibault Scoquart; Igor V. Gornyi; Alexander D. Mirlin

doi:10.1103/PhysRevB.109.214203

paper

Role of Fock-space correlations in many-body localization

arXiv:2402.10123 · doi:10.1103/PhysRevB.109.214203

Abstract

Models of many-body localization (MBL) can be represented as tight-binding models in the many-body Hilbert space (Fock space). We explore the role of correlations between matrix elements of the effective Fock-space Hamiltonians in the scaling of MBL critical disorder $W_{c} (n)$ with the size $n$ of the system. For this purpose, we consider five models, which all have the same distributions of diagonal (energy) and off-diagonal ("hopping") Fock-space matrix elements but different Fock-space correlations. These include quantum-dot (QD) and one-dimensional (1D) MBL models, their modifications (uQD and u1D models) with removed correlations of off-diagonal matrix elements, as well a quantum random energy model (QREM) with no correlations at all. Our numerical results are in full consistency with analytical arguments predicting $n^{3/4} (ln n)^{- 1/4} ≲ W_{c} ≲ n ln n$ for the scaling of $W_{c} (n)$ in the QD model (we find $W_{c} \sim n$ numerically), $W_{c} (n) \sim const.$ for the 1D model, $W_{c} \sim n ln n$ for the uQD and u1D models without off-diagonal correlations, and $W_{c} \sim n^{1/2} ln n$ for QREM. The key difference between the QD and 1D models is in the structure of correlations of many-body energies. Removing off-diagonal Fock-space correlations makes both these models "maximally chaotic". Our findings demonstrate that the scaling of $W_{c} (n)$ for MBL transitions is governed by a combined effect of Fock-space correlations of diagonal and off-diagonal matrix elements.

arXiv comment29 pages, 15 figures

Role of Fock-space correlations in many-body localization

Abstract

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