Dephasing Catastrophe in 4−ε Dimensions: A Possible Instability of the Ergodic (Many-Body-Delocalized) Phase
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In two dimensions, 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−ε dimensions, and find a nontrivial fixed point corresponding to a temperature T∗∼ε>0 where the dephasing time diverges. Assuming that this fixed point survives to ε=2, we associate it with 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.
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Liao, Yunxiang and Foster, Matthew S.. "Dephasing Catastrophe in 4−ε Dimensions: A Possible Instability of the Ergodic (Many-Body-Delocalized) Phase." Physical Review Letters, 120, no. 23 (2018) American Physical Society: https://doi.org/10.1103/PhysRevLett.120.236601.