From Bose glass to many-body localization in a one-dimensional disordered Bose gas

Abstract

We determine the finite-temperature phase diagram of a one-dimensional disordered Bose gas using bosonization and the nonperturbative functional renormalization group (RG). We discuss two different scenarios, based on distinct truncations of the effective action. In the first scenario, the Bose glass is destabilized at any finite temperature, giving rise to a normal fluid. Nevertheless, one can distinguish a low-temperature glassy regime, where disorder plays an important role on intermediate length and time scales, from a high-temperature regime, where disorder becomes irrelevant. In the second scenario, below a temperature $T_c$, the RG flow exhibits a singularity at a finite value of the RG momentum scale. We propose that this singularity signals a lack of thermalization and the existence of a localized phase for $T<T_c$. We provide a description of this low-temperature localized phase within a droplet picture and highlight a number of possible similarities with characteristics of many-body localized phases, including non-thermal behavior, avalanche instabilities and many-body resonances, the structure of the many-body spectrum, and slow dynamics in the ergodic phase. The normal fluid above $T_c$, and below a crossover temperature $T_g$, exhibits glassy properties on intermediate scales.

21 pages, 13 figures

References in corpus (15)

• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Exact evolution equation for the effective potential
• Localization of interacting fermions at high temperature
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Many-Body Localization in the Age of Classical Computing
• Purification and many-body localization in cold atomic gases
• Unified picture of superfluidity: From Bogoliubov's approximation to Popov's hydrodynamic theory
• Energy level dynamics across the many-body localization transition
• Quantum chaos and level dynamics
• The Effect of Randomness on the Mott State
• Cat states carrying long-range correlations in the many-body localized phase
• Superfluid--Bose-glass transition in a system of disordered bosons with long-range hopping in one dimension
• Mott-glass phase induced by long-range correlated disorder in a one-dimensional Bose gas