Dephasing catastrophe in $4 - \epsilon$ dimensions: A toy model for the ergodic to many-body-localized phase transition

摘要

In two dimensions (2D), dephasing by a bath cuts off Anderson localizationthat would otherwise occur at any energy density for fermions with disorder.For an isolated system with short-range interactions, the system can be its ownbath, exhibiting diffusive (non-Markovian) thermal density fluctuations. Werecast the dephasing of weak localization due to a diffusive bath as aself-interacting polymer loop. We investigate the critical behavior of the loopin $d=4-\epsilon$ dimensions, and find a nontrivial fixed point correspondingto temperature $T^* \sim \epsilon >0$ where the dephasing time diverges.Assuming this fixed point survives to $\epsilon=2$, we associate it with a toyversion of the ergodic to many-body-localized (MBL) phase transition in 2D.