Thouless Time Analysis of Anderson and Many-Body Localization Transitions

Abstract

Spectral statistics of disordered systems encode Thouless and Heisenberg time scales whose ratio determines whether the system is chaotic or localized. Identifying similarities between system size and disorder strength scaling of Thouless time for disordered quantum many-body systems with results for 3D and 5D Anderson models, we argue that the two-parameter scaling breaks down in the vicinity of the transition to the localized phase signalling subdiffusive dynamics.

Quantum chaos challenges many-body localization

“…Using an identical criterion one can reliably detect the well established Anderson localization transition in three (and higher) dimensions [12], thereby suggesting a link between the ergodicity breaking transition in disordered many-body systems and the Anderson localization transition.…”

“…A similar analysis to those in Figs. 2(c) and 2(f) has been recently performed for the three-dimensional (3d) and five-dimensional (5d) Anderson models [12]. It was shown that the critical disorder W c of the Anderson localization transition can be reliably detected using the same methodology as applied here, i.e., by requiring g = const when L increases (cf.…”

“…The timet Th can be viewed as an inverse of the energy scale that probes sensitivity of disordered systems to boundary conditions (as introduced by Edwards and Thouless [11]), and it is now commonly referred to as the time after which the quantum dynamics is universal and governed by random matrices. Following the latter definition oft Th , it has been recently shown that requiring t Th /t H = const when increasing the system size provides a very efficient tool to detect the localization transition point in the three and five dimensional Anderson models [12].…”

“…2. First, the ergodicity breaking transition in disordered many-body systems carries analogies with the Anderson localization transition [12], for which the transition point can be detected requiring lim L→∞ g(W * , L) = g * = const. Second, the scaling solution of g (and of other ergodicity indicators such as S and r [33]) obtained by requiring the optimal data collapse as a function of L/ξ BKT , provides an efficient method to pin the ergodicity breaking transition in finite systems.…”

Coexistence of localized and extended phases: Many-body localization in a harmonic trap

“…Such systems are directly amenable to experimental studies [18][19][20][21][22][23][24][25][26][27]. In this way we also stay away from a current vivid debate about the very existence of MBL in the thermodynamic limit [28][29][30][31][32]. We consider one-dimensional (1D) chains with chemical potentials quadratically dependent on position.…”