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

作者：Monthus Cecile^*

来源：Journal of Physics A-Mathematical and Theoretical, 2017, 50(9): 095002.

DOI：10.1088/1751-8121/aa583f

• many-body-localization
• energy level curvature
• fidelity

For disordered interacting quantum systems, the sensitivity of the spectrum to twisted boundary conditions depending on an infinitesimal angle phi can be used to analyze the many-body-localization transition. The sensitivity of the energy levels En( phi) is measured by the level curvature K-n= E-n('')(0), or more precisely by the Thouless dimensionless curvature k(n) = K-n/Delta(n), where Delta(n) is the level spacing that decays exponentially with the size L of the system. For instance Delta(n) alpha 2(-L) in the middle of the spectrum of quantum spin chains of L spins, while the Drude weight D-n = LKn studied recently by Filippone et al (arxiv:1606.07291v1) involves a different rescaling. The sensitivity of the eigenstates |psi(n)(phi)> is characterized by the susceptibility chi(n) = -F-n('')(0) of the fidelity F-n = | < psi(n)( 0)| psi n(phi)> |. Both observables are distributed with probability distributions displaying power-law tails P-beta(k) similar or equal to A(beta) |k|(-(2+beta)) and Q(chi) similar or equal to B-beta(-3+beta/2), where beta is the level repulsion index taking the values beta(GOE) = 1 in the ergodic phase and beta(loc) = 0 in the localized phase. The amplitudes A(beta) and B-beta 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).

• 出版日期2017-3-3
• 单位中国地震局