A microscopically motivated renormalization scheme for the MBL/ETH transition

Thiery, Thimothée; Müller, Markus; Roeck, Wojciech De

doi:10.48550/arxiv.1711.09880

Cited by 30 publications

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“…The phenomenology of l-bits explains many distinctive features of the MBL phase, including its unusual slow dynamics [8][9][10][11][12], and the possibility for novel forms of "localization protected" order in individual highly excited many-body eigenstates [13][14][15][16][17]. The phase transition between an MBL and a thermal phase is a new class of dynamical phase transition, a complete understanding of which has thus far proved to be notoriously elusive: analytical treatments are mainly tractable only under phenomenological frameworks [18][19][20][21][22][23][24][25][26] and numerical simulations are restricted to very small system sizes that do not exhibit the asymptotic physics of large systems [3,8,[27][28][29][30][31]. Thus an interesting complementary approach to the transition has been to try to understand mechanisms by which MBL can be destabilized under certain conditions, and to then build numerical evidence for such mechanisms, and develop corresponding phenomenological models to capture the large-scale consequences of those mechanisms.…”

Section: Introductionmentioning

confidence: 99%

“…Thus an interesting complementary approach to the transition has been to try to understand mechanisms by which MBL can be destabilized under certain conditions, and to then build numerical evidence for such mechanisms, and develop corresponding phenomenological models to capture the large-scale consequences of those mechanisms. This has been exhibited by a body of work that proposed "avalanches" seeded by rare Griffiths events as a mechanism for destabilizing MBL in disordered systems [32,33], attempted to numerically observe certain features of avalanches in minimal toy models [34][35][36], and determined the consequences of an avalanche-driven transition in phenomenological renormalization group (RG) treatments [22,24,26]. There have also recently been experiments investigating isolated avalanches in cold atomic systems [37].…”

Section: Introductionmentioning

confidence: 99%

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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: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Morningstar,

Colmenarez,

Khemani

et al. 2021

Preprint

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“…Instead of directly investigating rare thermal regions in a closed systems, let us study the transient dynamics of a system coupled to an infinite bath. For an infinite bath the system will definitely thermalize, but within the avalanche theory [15,16] it is the rate of thermalization that governs how large the thermal inclusions become. The argument is rather simple, consider a thermal inclusion of size ℓ 0 , and imagine it has been able to thermalize ℓ spins on both sides, then the inclusion has grown to a size ℓ 0 + 2ℓ.…”

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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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“…Moreover, while we have focused on coupling a twolevel system, or spin-1/2, to a bath, it would be useful to obtain results for higher dimensional qudits, and even pairs of large weakly coupled baths. The latter case in particular could prove relevant to the RG studies of the MBL transition [85][86][87][88][89][90][91], which currently treat pairs of thermal regions as either in the weak or strong coupling regimes. This is a poor approximation at large d where these regimes are asymptotically separated.…”

Section: Discussionmentioning

confidence: 99%

Partial thermalisation of a two-state system coupled to a finite quantum bath

Crowley,

Chandran

2021

Preprint

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The eigenstate thermalisation hypothesis (ETH) is a statistical characterisation of eigen-energies, eigenstates and matrix elements of local operators in thermalising quantum systems. We develop an ETH-like ansatz of a partially thermalising system composed of a spin-1 2 coupled to a finite quantum bath. The spin-bath coupling is sufficiently weak that ETH does not apply, but sufficiently strong that perturbation theory fails. We calculate (i) the distribution of fidelity susceptibilities, which takes a broadly distributed form, (ii) the distribution of spin eigenstate entropies, which takes a bi-modal form, (iii) infinite time memory of spin observables, (iv) the distribution of matrix elements of local operators on the bath, which is non-Gaussian, and (v) the intermediate entropic enhancement of the bath, which interpolates smoothly between zero and the ETH value of log 2. The enhancement is a consequence of rare many-body resonances, and is asymptotically larger than the typical eigenstate entanglement entropy. We verify these results numerically and discuss their connections to the many-body localisation transition.

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A microscopically motivated renormalization scheme for the MBL/ETH transition

Cited by 30 publications

References 0 publications

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

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

Markovian baths and quantum avalanches

Partial thermalisation of a two-state system coupled to a finite quantum bath

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