Distribution of higher order spacing ratios in one- plus two-body random matrix ensembles with spin symmetry

In this paper, we investigate the Anderson transition on random graphs by taking advantage of the knowledge on MBL. The numerous studies on the MBL transition, and in particular the difficulty of describing this phenomenon analytically starting from a microscopic model, have led to the development of an approach called the phenomenological renormalization group (RG) [46][47][48][49][50]. This approach is based on an avalanche mechanism thought to be responsible for an instability of MBL leading to a transition to a thermal phase [42,51]. The phenomenological RG allows to describe the renormalization flow in the vicinity of the MBL transition. Remarkably, recent studies have shown that this flow is of the Kosterlitz-Thouless type [48] (or at least very similar to it [50]). Thus, from the MBL side, we have precise analytical predictions of the flow and the nature of the transition. This is not the case for the Anderson transition on random graphs: although several critical properties are known, the flow and nature of the transition are not. The purpose of this paper is to remedy this. We will show that the flow of the Anderson transition is of Kosterlitz-Thouless type, extremely similar to the MBL transition,

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“…Following Refs. [156][157][158], we consider the distribution of non-overlapping higher order spacing ratios defined by…”

Section: W C νmentioning

confidence: 99%

Critical properties of the Anderson transition on random graphs: Two-parameter scaling theory, Kosterlitz-Thouless type flow, and many-body localization

et al. 2022

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“…These days, a very good alternative to NNSD called the ratio of level spacings [19] is gaining a lot of attraction [15,[20][21][22][23][24] as it is simple to compute and no unfolding is needed as it is independent of the form of the density of the energy levels. The higher orders of ratio of spacings have also been studied in [25,26]. The distribution intermediate of Poisson and GOE is described by Brody distribution [27].…”

Section: Introductionmentioning

confidence: 99%