Many-body-localization transition: sensitivity to twisted boundary conditions

Abstract

For disordered interacting quantum systems, the sensitivity of the spectrum to twisted boundary conditions depending on an infinitesimal angle ϕ can be used to analyze the many-body-localization transition. The sensitivity of the energy levels is measured by the level curvature , or more precisely by the Thouless dimensionless curvature , where is the level spacing that decays exponentially with the size L of the system. For instance in the middle of the spectrum of quantum spin chains of L spins, while the Drude weight studied recently by Filippone et al (arxiv:1606.07291v1) involves a different rescaling. The sensitivity of the eigenstates is characterized by the susceptibility of the fidelity . Both observables are distributed with probability distributions displaying power-law tails and , where β is the level repulsion index taking the values in the ergodic phase and in the localized phase. The amplitudes and of these two heavy tails are given by some moments of the off-diagonal matrix element of the local current operator between two nearby energy levels, whose probability distribution has been proposed as a criterion for the many-body-localization transition by Serbyn et al (2015 Phys. Rev. X 5 041047).