Dephasing catastrophe in $4-\epsilon$ dimensions: A possible instability of the ergodic (many-body-delocalized) phase

Abstract

In two dimensions (2D), dephasing by a bath cuts off Anderson localization that would otherwise occur at any energy density for fermions with disorder. For an isolated system with short-range interactions, the system can be its own bath, exhibiting diffusive (non-Markovian) thermal density fluctuations. We recast the dephasing of weak localization due to a diffusive bath as a self-interacting polymer loop. We investigate the critical behavior of the loop in $d=4-\epsilon$ dimensions, and find a nontrivial fixed point corresponding to a temperature $T^{\ast }\sim \epsilon >0$ where the dephasing time diverges. Assuming that this fixed point survives to $\epsilon =2$, we associate it to a possible instability of the ergodic phase. Our approach may open a new line of attack against the problem of the ergodic to many-body-localized phase transition in $d>1$ spatial dimensions.

11 pages, 5 figures

References in corpus (8)

• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Stability and instability towards delocalization in MBL systems
• Possible experimental manifestations of the many-body localization
• Multifractal analysis with the probability density function at the three-dimensional Anderson transition
• Topological protection, disorder, and interactions: Survival at the surface of 3D topological superconductors
• A mean-field theory of nearly many-body localized metals
• Response theory of the ergodic many-body delocalized phase: Keldysh Finkel'stein sigma models and the 10-fold way

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• Non-Markovian dephasing of disordered, quasi-one-dimensional fermion systems
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