Phenomenology of spectral functions in disordered spin chains at infinite temperature

Vidmar, Lev; Krajewski, Bartosz; Bonca, Janez; Mierzejewski, Marcin

doi:10.48550/arxiv.2105.09336

Cited by 6 publications

(7 citation statements)

References 74 publications

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“…We also note that recently there have been a number of papers expressing various levels of skepticism about the stability of the MBL phase in the limits of large systems and long times [44][45][46][47][48][49], and a number of challenges to those conclusions [50][51][52][53]. While our results do not support (nor directly contradict) any of these arguments against the existence of the MBL phase, our work was, in part, motivated by these challenges, which have at least demonstrated that our understanding of the MBL regime is still rather incomplete.…”

Section: Mbl Regimementioning

confidence: 94%

Avalanches and many-body resonances in many-body localized systems

Morningstar,

Colmenarez,

Khemani

et al. 2021

Preprint

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We numerically study both the avalanche instability and many-body resonances in stronglydisordered spin chains exhibiting many-body localization (MBL). We distinguish between a MBL-like regime at finite system sizes or times, and the asymptotic MBL phase. In both Floquet and Hamiltonian models, we identify some "landmarks" within the finite-size MBL regime. Our first landmark is an estimate of where the MBL phase becomes unstable to avalanches, obtained by measuring the slowest relaxation rate of a finite chain coupled to an infinite bath at one end. Our estimates indicate that the actual MBL-to-thermal phase transition, in the limit of an infinite length system, occurs much deeper in the MBL regime than has been suggested by most previous studies. Our other landmarks involve system-wide many-body resonances. We find that the effective matrix elements producing eigenstates with system-wide many-body resonances are enormously broadly distributed. This broad distribution means that the onset of such resonances in typical samples occurs quite deep in the MBL regime, and the first such resonances typically involve rare pairs of eigenstates that are farther apart in energy than the minimum gap. Thus we find that the resonance properties define two landmarks that divide the MBL regime of finite-size systems in to three subregimes: (i) at strongest randomness, typical samples do not have any eigenstates that are involved in system-wide many-body resonances; (ii) there is a substantial intermediate regime where typical samples do have such resonances, but the pair of eigenstates with the minimum spectral gap does not, so that the size of the minimum gap agrees with expectations from Poisson statistics; and (iii) in the weaker randomness regime, the minimum gap is larger than predicted by Poisson level statistics because it is involved in a many-body resonance and thus subject to level repulsion. Nevertheless, even in this third subregime, all but a vanishing fraction of eigenstates remain non-resonant and the system thus still appears MBL in many respects. Based on our estimates of the location of the avalanche instability, it might be that the MBL phase is only part of subregime (i), and the other subregimes are entirely in the thermal phase, even though they look localized in many respects at numerically accessible system sizes.

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Section: Mbl Regimementioning

confidence: 94%

Avalanches and many-body resonances in many-body localized systems

Morningstar,

Colmenarez,

Khemani

et al. 2021

Preprint

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“…This makes understanding of ergodic to MBL transition a formidable undertaking, especially in conjunction with non-perturbative mechanisms of delocalization of MBL phase [21][22][23]. Despite intensive research [20,[24][25][26][27][28][29][30][31][32][33][34][35][36] the status of the MBL phase is not fully understood as shown by the recent debate about the stability of MBL [37][38][39][40][41][42][43][44][45]. On the other hand, the existence of MBL is essentially certified in sufficiently strongly disordered spin chains as shown in [46,47].…”

Section: Introductionmentioning

confidence: 99%

Finite-Size scaling analysis of many-body localization transition in quasi-periodic spin chains

Aramthottil,

Chanda,

Sierant

et al. 2021

Preprint

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We analyze the finite-size scaling of the average gap-ratio and the entanglement entropy across the many-body localization (MBL) transition in one dimensional Heisenberg spin-chain with quasiperiodic (QP) potential. By using the recently introduced cost-function approach, we compare different scenarios for the transition using exact diagonalization of systems up to 22 lattice sites. Our findings suggest that the MBL transition in the QP Heisenberg chain belongs to the class of Berezinskii-Kosterlitz-Thouless (BKT) transition, the same as in the case of uniformly disordered systems as advocated in recent studies. Moreover, we observe that the critical disorder strength shows a clear sub-linear drift with the system-size as compared to the linear drift seen in random disordered models, suggesting that the finite-size effects in the MBL transition for the QP systems are less severe than that in the random disordered scenario. Moreover, deep in the ergodic regime, we find an unexpected double-peak structure of distribution of on-site magnetizations that can be traced back to the strong correlations present in the QP potential.

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“…Recently, a number of works have questioned the stability of the MBL phase [3][4][5][6][7][8]. In turn, some of the conclusions were challenged by follow up papers [9][10][11][12][13].…”

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confidence: 99%

Markovian baths and quantum avalanches

Sels

2021

Preprint

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In this work I will discuss some numerical results on the stability of the many-body localized phase to thermal inclusions. The work simplifies a recent proposal by Morningstar et al. [arXiv:2107.05642] and studies small disordered spin chains which are perturbatively coupled to a Markovian bath. The critical disorder for avalanche stability of the canonical disordered Heisenberg chain is shown to exceed W * 20. In stark contrast to the Anderson insulator, the avalanche threshold drifts considerably with system size, with no evidence of saturation in the studied regime. I will argue that the results are most easily explained by the absence of a many-body localized phase.

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Phenomenology of spectral functions in disordered spin chains at infinite temperature

Cited by 6 publications

References 74 publications

Avalanches and many-body resonances in many-body localized systems

Avalanches and many-body resonances in many-body localized systems

Finite-Size scaling analysis of many-body localization transition in quasi-periodic spin chains

Markovian baths and quantum avalanches

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