Many-body localization as a large family of localized ground states

Dupont, Maxime; Laflorencie, Nicolas

doi:10.1103/physrevb.99.020202

Cited by 26 publications

(19 citation statements)

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“…All eigenfunctions of (3.1) are localized for any h = 0. Using such localized eigenstates |Ψ loc as an input states yield a vanishing variance e 3 when L → +∞, a feature already observed for the zerotemperature interacting Bose-glass problem [5]. Therefore, we expect |Ψ loc to be a fairly good approximant of an eigenstate of the associated parent Hamiltonian H P , encoded in the corresponding eigenvector x 3 of C. This becomes increasingly true for growing disorder strength and system size.…”

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confidence: 56%

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From eigenstate to Hamiltonian: Prospects for ergodicity and localization

2019

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This work addresses the so-called inverse problem which consists in searching for (possibly multiple) parent target Hamiltonian(s), given a single quantum state as input. Starting from Ψ0, an eigenstate of a given local Hamiltonian H0, we ask whether or not there exists another parent Hamiltonian HP for Ψ0, with the same local form as H0. Focusing on one-dimensional quantum disordered systems, we extend the recent results obtained for Bose-glass ground states [M. Dupont and N. Laflorencie, Phys. Rev. B 99, 020202(R) (2019)] to Anderson localization, and the manybody localization (MBL) physics occurring at high-energy. We generically find that any localized eigenstate is a very good approximation for an eigenstate of a distinct parent Hamiltonian, with an energy variance σ 2 P (L) = H 2 P Ψ 0 − HP 2 Ψ 0 vanishing as a power-law of system size L. This decay is microscopically related to a chain breaking mechanism, also signalled by bottlenecks of vanishing entanglement entropy. A similar phenomenology is observed for both Anderson and MBL. In contrast, delocalized ergodic many-body eigenstates uniquely encode the Hamiltonian in the sense that σ 2 P (L) remains finite at the thermodynamic limit, i.e., L → +∞. As a direct consequence, the ergodic-MBL transition can be very well captured from the scaling of σ 2 P (L).

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Section: )supporting

confidence: 56%

“…h 1 2 3 4 5 α =0 2.05(1) 2.47(1) 3.10(1) 3.56(1) 3.88(1) α =0. 5 2.05(1) 2.24(1) 2.61(1) 2.93(1) 3.20 (1) TABLE I. Decay exponent α(h) of the third eigenvalue e3 of the covariance matrix, as defined in Eq.…”

Section: )mentioning

confidence: 99%

From eigenstate to Hamiltonian: Prospects for ergodicity and localization

2019

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“…For the standard Heisenberg model with RD, the probability distribution P(s z ) for site-resolved spin expectation values s z l = Ŝz l for mid-energy eigenstates ( ≈ 0.5) has a U-shape with peaks at s z ±0.5 in the MBL phase due to the presence of local integrals of motion that have substantial overlaps with Ŝz l operators [61,[88][89][90][91]. According to the eigenstate thermalization hypothesis, P(s z ) has a Gaussian distribution with a peak at s z = 0 and variance that quickly decreases with L deep in the ergodic regime.…”

Section: Model and Observablesmentioning

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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“…Having characterized our zero-temperature phase transition, and in view of the recent evidence that localized ground states correspond to many-body localized excited eigenstates of related Hamiltonians 42 , we hope our model may be useful to shed light on the nature of the many-body localization transition, which remains largely unclear 4,5 .…”

Section: Discussionmentioning

confidence: 99%

Emergent dimerization and localization in disordered quantum chains

Vieira

Hoyos

2018

Phys. Rev. B

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We uncover a novel mechanism for inducing a gapful phase in interacting many-body quantum chains. The mechanism is nonperturbative, being triggered only in the presence of both strong interactions and strong aperiodic (disordered) modulation. In the context of the critical antiferromagnetic spin-1/2 XXZ chain, we identify an emerging dimerization which removes the system from criticality and stabilizes the novel phase. This mechanism is shown to be quite general in strongly interacting quantum chains in the presence of strongly modulated quasiperiodic disorder which is, surprisingly, perturbatively irrelevant. Finally, we also characterize the associated quantum phase transition via the corresponding critical exponents and thermodynamic properties. arXiv:1804.05108v4 [cond-mat.str-el]

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Many-body localization as a large family of localized ground states

Cited by 26 publications

References 70 publications

From eigenstate to Hamiltonian: Prospects for ergodicity and localization

From eigenstate to Hamiltonian: Prospects for ergodicity and localization

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

Emergent dimerization and localization in disordered quantum chains

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