A Memory Hierarchy for Many-Body Localization: Emulating the Thermodynamic Limit

Abstract

Local memory -the ability to extract information from a subsystem about its initial state -is a central feature of many-body localization. We introduce, investigate, and compare several informationtheoretic quantifications of memory and discover a hierarchical relationship among them. We also find that while the Holevo quantity is the most complete quantifier of memory, vastly outperforming the imbalance, its decohered counterpart is significantly better at capturing the critical properties of the many-body localization transition at small system sizes. This motivates our suggestion that one can emulate the thermodynamic limit by artifically decohering otherwise quantum quantities. Applying this method to the von Neumann entropy results in critical exponents consistent with analytic predictions, a feature missing from similar small finite-size system treatments. In addition, the decohering process makes experiments significantly simpler by avoiding quantum state tomography.

Floquet-induced localization in long-range many-body systems

“…Introduction.-Many-Body Localization (MBL) is a profound concept in condensed matter physics for breaking the ergodicity principle [1][2][3][4][5][6][7][8][9]. To better understand the different aspects of MBL, several quantum information concepts [10][11][12][13][14][15][16] have been theoretically developed and several experiments on newly emerging quantum simulators have been performed [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Most of the MBL literature have been dedicated to 1D short-range interactions, however, several fundamental problems remain open for systems with long-range couplings [34,35].…”

“…For the sake of completeness, in Table I, we provide the estimated values of γ for both uniform and nonuniform couplings [38]. Dynamics of Imbalance.-While in the ergodic phase, the imbalance has to saturate to zero, showing no memory about the initial state, in the MBL phase it reaches a finite value, resembling the memory of its initial state [13,28,31]. Fig.…”