Abstract
Recent experiments in quantum simulators have provided evidence for the Many-Body Localized (MBL) phase in 1D and 2D bosonic quantum matter. The theoretical study of such bosonic MBL, however, is a daunting task due to the unbounded nature of its Hilbert space. In this work, we introduce a method to compute the long-time real-time evolution of 1D and 2D bosonic systems in an MBL phase at strong disorder and weak interactions. We focus on local dynamical indicators that are able to distinguish an MBL phase from an Anderson localized one. In particular, we consider the temporal fluctuations of local observables, the spatiotemporal behavior of two-time correlators and Out-Of-Time-Correlators (OTOCs). We show that these few-body observables can be computed with a computational effort that depends only polynomially on system size but is independent of the target time, by extending a recently proposed numerical method [Phys. Rev. B 99, 241114 (2019)] to mixed states and bosons. Our method also allows us to surrogate our numerical study with analytical considerations of the time-dependent behavior of the studied quantities.
Highlights
Many-body localization (MBL), which generalizes the concept of Anderson localization (AL) [1] to the interacting regime, is a quantum phenomenon where an isolated quantum many-body system fails to reach thermal equilibrium, evading the eigenstate thermalization hypothesis [2,3,4]
We focus on local dynamical indicators that are able to distinguish an many-body localized (MBL) phase from an Anderson localized one
We find that bosonic MBL systems exhibit a logarithmic lightcone for information propagation [see Figs. 1(a) and 1(b) for the of-time-ordered correlators (OTOCs) in 1D and 2D, respectively]
Summary
Many-body localization (MBL), which generalizes the concept of Anderson localization (AL) [1] to the interacting regime, is a quantum phenomenon where an isolated quantum many-body system fails to reach thermal equilibrium, evading the eigenstate thermalization hypothesis [2,3,4]. An MBL system retains the memory of its initial conditions, which can be probed by the preservation local observables, the simplest being particle occupations of lattice sites It has emerged as a novel paradigm for ergodicity breaking of generic many-body systems subject to strong disorder [5,6,7,8]. For fermionic and spin systems it is understood that interactions induce a dephasing mechanism, which allows entanglement and quantum correlations to spread during the dynamics, even though transport is absent [19,37,38]. III D, we study the dependency of these observables on the occupation amplitude, a property unique to bosonic systems
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