Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain

Laflorencie, Nicolas; Lemarié, Gabriel; Macé, Nicolas

doi:10.48550/arxiv.2004.02861

Cited by 11 publications

(18 citation statements)

References 103 publications

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“…More generally, the double-peak U-shape structure observed in Fig. 5 (b) in the disordered phase is also observed in the context of many-body localization at high energy, and is a fingerprint of ergodicity breaking [146][147][148][149][150]. In Fig.…”

Section: Real-space and Ergodicity Properties A Local Density Of Bosonssupporting

confidence: 61%

“…The finite-size scaling analysis of localization transitions in graphs of effective infinite dimensionality such as the Cayley tree is particularly subtle. This was illustrated recently in the Anderson transition on random graphs [20,21,34], in the MBL transition [145,150] and in certain classes of random matrices [33,158,159]. The difficulty comes from the fact that the volume of the system N (the number of sites) varies exponentially with the linear size of the system, i.e., the number of generations G in the Cayley tree.…”

Section: A Scaling Analysis Across the Transitionmentioning

confidence: 99%

“…In particular, a linear scaling can imply (depending on the critical behavior) a non-ergodic delocalized phase, see Refs. [20,34,145,150].…”

Section: A Scaling Analysis Across the Transitionmentioning

confidence: 99%

“…We detail this analysis in this section. The approach we have used is very similar to what has been done in the context of Anderson localization on random graphs and the MBL transition [20,34,145,150]. We assume some value of µ c which belongs to the set of µ's that we have simulated.…”

Section: A Scaling Analysis Across the Transitionmentioning

confidence: 99%

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Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking

Dupont,

Laflorencie,

Lemarié

2020

Preprint

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Building on large-scale quantum Monte Carlo simulations, we investigate the zero-temperature phase diagram of hard-core bosons in a random potential on site-centered Cayley trees with branching number K = 2. In order to follow how the Bose-Einstein condensate (BEC) is affected by the disorder, we focus on both the zero-momentum density, probing the quantum coherence, and the one-body density matrix (1BDM) whose largest eigenvalue monitors the off-diagonal long-range order. We further study its associated eigenstate which brings useful information about the real-space properties of this leading eigenmode. Upon increasing randomness, we find that the system undergoes a quantum phase transition at finite disorder strength between a long-range ordered BEC state, fully ergodic at large scale, and a new disordered Bose glass regime showing conventional localization for the coherence fraction while the 1BDM displays a non-trivial algebraic vanishing BEC density together with a non-ergodic occupation in real-space. These peculiar properties can be analytically captured by a simple toy-model on the Cayley tree which provides a physical picture of the Bose glass regime.

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Section: Real-space and Ergodicity Properties A Local Density Of Bosonssupporting

confidence: 61%

Section: A Scaling Analysis Across the Transitionmentioning

confidence: 99%

“…In particular, a linear scaling can imply (depending on the critical behavior) a non-ergodic delocalized phase, see Refs. [20,34,145,150].…”

Section: A Scaling Analysis Across the Transitionmentioning

confidence: 99%

Section: A Scaling Analysis Across the Transitionmentioning

confidence: 99%

See 2 more Smart Citations

Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking

Dupont,

Laflorencie,

Lemarié

2020

Preprint

Self Cite

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show abstract

“…They also showed that the numerical results from the earlier RGs are quite consistent with this scenario, even though they had been instead fit to one-parameter scaling. The conventional scaling assumptions used for exact calculations on small systems are also starting to be revisited [28,29]. In Ref.…”

Section: √ Ymentioning

confidence: 99%

Many-body localization near the critical point

Morningstar,

Huse,

Imbrie

2020

Preprint

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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.

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Subdiffusion in a one-dimensional Anderson insulator with random dephasing: Finite-size scaling, Griffiths effects, and possible implications for many-body localization

Taylor

Scardicchio

2021

Phys. Rev. B

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We study transport in the boundary-driven XX spin chain with onsite disorder and randomly positioned onsite dephasing, observing a transition from diffusive to subdiffusive spin transport below a critical density of sites with dephasing. We then present an exactly solvable semiclassical model of conductors and insulators, which exhibits both diffusive and subdiffusive phases, and qualitatively reproduces the results of the quantum system. The subdiffusion in these models is a consequence of rare insulating regions, and they therefore exhibit, in a more controlled setup, the physics of "Griffiths effects" which have been conjectured to cause the subdiffusive transport observed in interacting many-body localizable systems. For the quantum model we show that finitesize effects come from the interplay of three characteristic lengths: one associated with disorder (the localization length), one with dephasing, and the third with the percolation problem defining large, rare, insulating regions. The latter grows logarithmically with system size, and we conjecture that this may be the reason why the heavy-tailed distributions typical of Griffiths effects have not been observed in subdiffusive interacting systems.

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Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain

Cited by 11 publications

References 103 publications

Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking

Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking

Many-body localization near the critical point

Subdiffusion in a one-dimensional Anderson insulator with random dephasing: Finite-size scaling, Griffiths effects, and possible implications for many-body localization

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