Logarithmic growth of local entropy and total correlations in many-body localized dynamics

Abstract

The characterizing feature of a many-body localized phase is the existence of an extensive set of quasilocal conserved quantities with an exponentially localized support. This structure endows the system with the signature logarithmic in time entanglement growth between spatial partitions. This feature differentiates the phase from Anderson localization, in a non-interacting model. Experimentally measuring the entanglement between large partitions of an interacting many-body system requires highly non-local measurements which are currently beyond the reach of experimental technology. In this work we demonstrate that the defining structure of many-body localization can be detected by the dynamics of a simple quantity from quantum information known as the total correlations which is connected to the local entropies. Central to our finding is the necessity to propagate specific initial states, drawn from the Hamiltonian unbiased basis (HUB). The dynamics of the local entropies and total correlations requires only local measurements in space and therefore is potentially experimentally accessible in a range of platforms.The study of transport properties of quantum systems is a topic of paramount importance in condensed matter physics. A crucial aspect is the presence of disorder due to defects and irregularities in the material under study. In a celebrated work [1] Anderson showed how the presence of strong disorder can completely suppress transport of non-interacting electrons in a tight-binding model. Understanding the fate of this localisation phenomenon in the presence of interactions has seen an unprecedented revival in recent years [2,3]. In a seminal contribution Basko et. al. [4] argued that such phenomenon is stable when interactions between particles are introduced, showing the existence of a new dynamical phase of matter, the Many-Body Localized (MBL) phase [5][6][7][8] which, like its single particle counterpart exhibits a lack of both transport and thermalization [8]. From the experimental perspective, signatures of MBL physics have recently been observed in a number of different laboratories in cold atoms [9-11], ion traps [12] and NMR [13].As the system fails to thermalize, local observables retain memory of their initial conditions. In the last ten years there has been a large amount of effort devoted to the understanding of the MBL phase [2,5,[14][15][16][17][18]. The defining feature of an MBL state (e.g. as opposed to Anderson localization) has been identified in the fact that, while the transport of energy and local quantities is suppressed [19][20][21][22][23][24][25][26], there is transport of quantum information, occurring on a logarithmic time scale manifested in the growth of the half-chain entanglement entropy [27,28]. This behaviour can be explained by the emergence of an extensive set of quasi-local integrals of motions (Q-LIOMs) [18,[28][29][30]. Such objects have a support which is exponentially localized, the localization length being ξ. In the high-disorder regime the tails become more...

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