Many-body localization near the critical point

Abstract

We examine the many-body localization (MBL) phase transition in one-dimensional quantum systems with quenched randomness and short-range interactions. Following recent works, we use a strong-randomness renormalization group (RG) approach where the phase transition is due to the socalled avalanche instability of the MBL phase. We show that the critical behavior can be determined analytically within this RG. On a rough qualitative level the RG flow near the critical fixed point is similar to the Kosterlitz-Thouless (KT) flow as previously shown, but there are important differences in the critical behavior. Thus we show that this MBL transition is in a new universality class that is different from KT. The divergence of the correlation length corresponds to critical exponent ν → ∞, but the divergence is weaker than for the KT transition.

Universal spectral form factor for many-body localization

“…[20] pointed out that their claim of the absence of MBL is due to their choice of scaling function, which instead should follow a Kosteritz-Thouless "like" scaling form as they demonstrate in Ref. [24] consistent with recent theories of the MBL transition [25][26][27]. Irrespective of the question of validity of the finite-size numerics in the vicinity of the MBL transition, the question of how to characterize the MBL phase using the SFF alone, is undoubtedly worthy of further examination.…”

Effective dissipation rate in a Liouvillean graph picture of high-temperature quantum hydrodynamics

“…And when and how does hydrodynamics break down? A theory of how hydrodynamics emerges from generic unitary dynamics will bear on many other open questions, from the nature of the many body localization transition [4] [ [5][6][7][8][9][10][11][12][13] to experimental studies of the phase diagram of QCD [14] [ [15][16][17][18][19] . Many lines of evidence suggest that for generic spin systems-that is, systems not close to any kind of integrability or localization-dissipative hydrodynamics results from an insensitivity of local dynamics to long-range correlations.…”

Localization on Certain Graphs with Strongly Correlated Disorder

“…Efforts to understand the MBL phase and the accompanying MBL transition have ranged from extensive numerical studies [7,9,10] and phenomenological treatments [11][12][13][14][15][16] to studying the problem directly on the Fock space [17][18][19][20][21][22][23][24][25][26][27]. One virtue of the latter is that the problem can be cast as a disordered hopping problem on the Fock-space graph, thus offering the prospect of exploiting techniques and understandings developed for AL.…”