Localization and chaos in a quantum spin glass model in random longitudinal fields: Mapping to the localization problem in a Bethe lattice with a correlated disorder

Burin, Alexander L.

doi:10.1002/andp.201600292

Cited by 29 publications

(62 citation statements)

References 54 publications

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“…The family of p-spin models has a long history in the field of spin-glasses, both classical [47,[57][58][59][60][61] as well as quantum [62,63]. More recently, they have attracted attention in the context of ergodicity breaking and manybody localisation [64][65][66]. In the following we show that for the incarnation of the p-spin model considered, the distributions of Fock-space site energies are multivariate Gaussians, such that the rescaled covariances ρ r → 1 for finite r in the thermodynamic limit.…”

Section: B P-spin Modelsmentioning

confidence: 99%

Fock-space correlations and the origins of many-body localization

Roy

Logan

2020

Phys. Rev. B

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We consider the problem of many-body localisation on Fock space, focussing on the essential features of the Hamiltonian which stabilise a localised phase. Any many-body Hamiltonian has a canonical representation as a disordered tight-binding model on the Fock-space graph. The underlying physics is however fundamentally different from that of conventional Anderson localisation on high-dimensional graphs because the Fock-space graph possesses non-trivial correlations. These correlations are shown to lie at the heart of whether or not a stable many-body localised phase can be sustained in the thermodynamic limit, and a theory is presented for the conditions the correlations must satisfy for a localised phase to be stable. Our analysis is rooted in a probabilistic, self-consistent mean-field theory for the local Fock-space propagator and its associated self-energy; in which the Fock-space correlations, together with the extensive nature of the connectivity of Fock-space nodes, are key ingredients. The origins of many-body localisation in typical local Hamiltonians where the correlations are strong, as well as its absence in uncorrelated random energy-like models, emerge as predictions from the same overarching theory. To test these, we consider three specific microscopic models, first establishing in each case the nature of the associated Fock-space correlations. Numerical exact diagonalisation is then used to corroborate the theoretical predictions for the occurrence or otherwise of a stable many-body localised phase; with mutual agreement found in each case. CONTENTS

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Section: B P-spin Modelsmentioning

confidence: 99%

Fock-space correlations and the origins of many-body localization

Roy

Logan

2020

Phys. Rev. B

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“…Ref. [43]); on the other hand, the more complicated spin excitations possess the smaller probability of resonance, and, therefore, we do not expect them to modify the critical disordering estimated for quartets. Indeed, for n-spin resonances, one can estimate their amplitude using (n − 1) st order of perturbation theory (e. g. simultaneous transitions of the first spin with n − 1 other spins) as…”

Section: Multi-spin Clustersmentioning

confidence: 69%

“…According to Ref. [43], it is sufficient to have few resonances per system, if the diagonal interaction between them, U * , exceeds the typical resonant coupling strength, V * . Then the delocalization transition can be described using the similarity of the present problem with the localization problem on the Bethe lattice, with resonant coupling V * , disordering W , and coordination number N * [44].…”

Section: A General Definition Of the Localization Thresholdmentioning

confidence: 99%

“…Then the delocalization transition can be described using the similarity of the present problem with the localization problem on the Bethe lattice, with resonant coupling V * , disordering W , and coordination number N * [44]. The transition is detemined as [43]…”

Section: A General Definition Of the Localization Thresholdmentioning

confidence: 99%

“…Since amplitudes V * for different spin transitions can fluctuate, one can define the typical amplitude V * as the average absolute value of contributing amplitudes similarly to Refs. [43,44].…”

Section: A General Definition Of the Localization Thresholdmentioning

confidence: 99%

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Many-body localization in spin chains with long-range transverse interactions: Scaling of critical disorder with system size

Maksymov

Burin

2020

Phys. Rev. B

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We investigate many-body localization in the chain of interacting spins with a transverse powerlaw interaction, J0/r α , and random on-site potentials, φi ∈ (−W/2, W/2), in the long-range limit, α < 3/2, which has been recently examined experimentally on trapped ions. The many-body localization threshold is characterized by the critical disordering, Wc, which separates localized (W > Wc) and chaotic (W < Wc) phases. Using the analysis of the instability of localized states with respect to resonant interactions complemented by numerical finite size scaling, we show that the critical disordering scales with the number of spins, N , as Wc ≈ [1.37J0/(4/3 − α)]N 4/3−α ln N for 0 < α ≤ 1, and as Wc ≈ [J0/(1 − 2α/3)]N 1−2α/3 ln 2/3 N for 1 < α < 3/2 while the transition width scales as σW ∝ Wc/N . We use this result to predict the spin long-term evolution for a very large number of spins (N = 50), inaccessible for exact diagonalization, and to suggest the rescaling of hopping interaction with the system size to attain the localization transition at finite disordering in the thermodynamic limit of infinite number of spins.

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