Abstract
Inspired by recent experiments on many-body localized systems coupled to an environment, we apply a Flow Equation method to study the problem of a disorder chain of spinless fermions, coupled via density-density interactions to a second clean chain of spinless fermions. In particular, we focus on the conditions for the onset of a many-body localized phase in the clean sector of our model by proximity to the dirty one. We find that a many-body localization proximity effect in the clean component is established when the density of dirty fermions exceeds a threshold value. From the flow equation method we find that, similar to many-body localization in a single chain, the many-body localization proximity effect is also described by an extensive set of local integrals of motion. Furthermore, by tuning the geometry of the inter-chain couplings, we show that the dynamics of the model is ruled, on intermediate time scales, by an emergent set of quasi-conserved charges.
Highlights
The advent of cold gas experiments [1] has revitalized interest in fundamental questions of quantum thermodynamics in isolated many-body systems
In the case of many-body localization (MBL) systems, a guiding insight in fixing the variational ansatz for the flow equations comes from the l-bit picture [59, 60], which provides a method to numerically solve the flow in an efficient way: only the first leading terms describing pairwise interactions between the l-bits are retained, while higher order effects are truncated and discarded
We focus on the limit in which the disordered system would be strongly localized and vary the inter-chain coupling, clean chain hopping strength and reference state parameters
Summary
The advent of cold gas experiments [1] has revitalized interest in fundamental questions of quantum thermodynamics in isolated many-body systems. In addition to being able to study regimes of strong system-bath coupling, the flow equation method is able to access system’s sizes beyond those treatable in exact diagonalization, when disorder is sufficiently strong This approach allows us to establish the existence of the MBL proximity effect, and its consistency with a diagonal l-bit Hamiltonian of local conserved charges, in a wide range of parameters. We consider the case of a dirty chain of fermions, coupled every δ > 1 sites, to the clean one (see Fig. 6); the dirty chain acts as a distribution of impurities placed every δ sites, cutting the clean chain into a sequence of emergent integrals of motions These conserved charges lead to non-ergodic dynamics on intermediate time scales but are destroyed when interactions between conserved charges becomes effective. At these longer time scales, instead, the dynamics cross over from non-ergodic behavior to thermal behavior
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