Abstract
A number of experimental platforms for quantum simulations of disordered quantum matter, from dipolar systems to trapped ions, involve degrees of freedom which are coupled by power-law decaying hoppings or interactions, yet the interplay of disorder and interactions in these systems is far less understood than in their short-ranged counterpart. Here we consider a prototype model of interacting fermions with disordered long-ranged hoppings and interactions, and use the flow equation approach to map out its dynamical phase diagram as a function of hopping and interaction exponents. We demonstrate that the flow equation technique is ideally suited to problems involving long-range couplings due to its ability to accurately simulate very large system sizes. We show that, at large on-site disorder and for short-range interactions, a transition from a delocalized phase to a quasi many-body localized (MBL) phase exists as the hopping range is decreased. This quasi-MBL phase is characterized by intriguing properties such as a set of emergent conserved quantities which decay algebraically with distance. Surprisingly we find that a crossover between delocalized and quasi-MBL phases survives even in the presence of long-range interactions.
Highlights
Recent years have seen tremendous progress in our understanding of how isolated quantum many-body systems approach thermal equilibrium or fail to do so, sparking great interest in the possibility of engineering exotic nonergodic phases of quantum matter [1,2,3,4]
We are in position to present the main results of this work, concerning the effect of long-range couplings on manybody Anderson localization (MBL) physics as encoded in the model in Eq (1)
Though short-lived, this plateau is intriguing as it suggests that long-range interactions may weakly stabilize localization at short times. Having examined their effects separately, we compute the imbalance in the presence of both long-ranged interactions and long-range hopping and obtain the qualitative phase diagram shown in Fig. 7, where we show the imbalance I (t ) at a time t∗ = 100 after the quench as a function of α, β and superimpose lines at fixed imbalance as a guide to the eye
Summary
Recent years have seen tremendous progress in our understanding of how isolated quantum many-body systems approach thermal equilibrium or fail to do so, sparking great interest in the possibility of engineering exotic nonergodic phases of quantum matter [1,2,3,4] The interest around this question has substantially broadened across disciplines, evolving from a purely speculative issue in the foundation of quantum statistical mechanics [5] to a central topic of modern research, from condensed matter [6] to high-energy physics [7,8], with direct implications for the robustness of future quantum technologies.
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