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−ϵ dimensions, and find a nontrivial fixed point corresponding to temperature
T∗∼ϵ>0 where the dephasing time diverges. Assuming this fixed point survives to
ϵ=2, we associate it with a toy version of the ergodic to many-body-localized (MBL) phase transition in 2D.
Many-body localization (MBL) addresses (de)localization in highly excited states of disordered interacting systems. The authors explore eigenstate correlations in the vicinity of the MBL transition, emphasizing that they can be measured on state-of-the-art quantum processors and simulators. In addition to the genuine many-body problem, localization on random regular graphs is considered, which serves as a toy model of the transition. Both models show remarkably similar behavior that includesergodicity of the delocalized phase, power-law enhancement of correlations at low frequency in the MBL phase, and maximalcorrelation between adjacent-in-energy states at the transition point.
The nature of the dynamical quantum phase transition between the many-body localized (MBL) phase and the thermal phase remains an open question, and one line of attack on this problem is to explore this transition numerically in finite-size systems. To maximize the contrast between the MBL phase and the thermal phase in such finite-size systems, we argue one should choose a Floquet model with no local conservation laws and rapid thermalization to ``infinite temperature'' in the thermal phase. Here we introduce and explore such a Floquet spin chain model and show that standard diagnostics of the MBL-to-thermal transition behave well in this model even at modest sizes. We also introduce a physically motivated space-time correlation function, which peaks at the transition in the Floquet model, but is strongly affected by conservation laws in Hamiltonian models.