Many-body localization transition in Rokhsar-Kivelson-type wave functions

Chen, Xiao; Yu, Xiongjie; Cho, Gil Young; Clark, Bryan K.; Fradkin, Eduardo

doi:10.1103/physrevb.92.214204

Cited by 23 publications

(31 citation statements)

References 72 publications

(80 reference statements)

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“…We use a 2N-bit binary number to represent the σ z basis. In the example of N = 3, the σ z basis wavefunction wavefunction elements are If we store ψ ij n ↑ in a row vector, then the index of ψ will be (1,2,3,4,5,6,7,11,12,13,8,9,10,14,15,16,17,18,19,20)…”

Section: Appendix A: Channel-state Dualitymentioning

confidence: 99%

“…A multitude of previous works has estab-lished the differences of these two classes of systems regarding aspects of the eigenvalues and eigenvectors of the Hamiltonian, exhibiting e.g. volume-vs area-law entanglement entropy [10][11][12][13][14][15][16] and the validity or violation 15,17,18 of the eigenstate thermalization hypothesis [19][20][21] , all revealing properites of the Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

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Operator entanglement entropy of the time evolution operator in chaotic systems

2017

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We study the growth of the operator entanglement entropy (EE) of the time evolution operator in chaotic, many-body localized (MBL) and Floquet systems. In the random field Heisenberg model we find a universal power law growth of the operator EE at weak disorder, a logarithmic growth at strong disorder, and extensive saturation values in both cases. In a Floquet spin model, the saturation value after an initial linear growth is identical to the value of a random unitary operator (the Page value). We understand these properties by mapping the operator EE to a global quench problem evolved with a similar parent-Hamiltonian in an enlarged Hilbert space with the same chaotic, MBL and Floquet properties as the original Hamiltonian. The scaling and saturation properties reflect the spreading of the state EE of the corresponding time evolution. We conclude that the EE of the evolution operator should characterize the propagation of information in these systems.

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Section: Appendix A: Channel-state Dualitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Operator entanglement entropy of the time evolution operator in chaotic systems

2017

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“…As in Anderson transitions where the critical point is characterized by multifractal eigenfunctions [47], one expects that the MBL transition is related to some multifractal properties [46,[74][75][76][77][78][79]. Besides the entanglement entropy described above, it is thus interesting to characterize the statistics of the whole entanglement spectrum of Equation (38), both in the many-body localized phase b > 1 and at the critical point b c = 1.…”

Section: Multifractal Statistics Of the Entanglement Spectrummentioning

confidence: 99%

Many-Body-Localization Transition in the Strong Disorder Limit: Entanglement Entropy from the Statistics of Rare Extensive Resonances

Monthus

2016

Entropy

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Abstract:The space of one-dimensional disordered interacting quantum models displaying a many-body localization (MBL) transition seems sufficiently rich to produce critical points with level statistics interpolating continuously between the Poisson statistics of the localized phase and the Wigner-Dyson statistics of the delocalized phase. In this paper, we consider the strong disorder limit of the MBL transition, where the level statistics at the MBL critical point is close to the Poisson statistics. We analyze a one-dimensional quantum spin model, in order to determine the statistical properties of the rare extensive resonances that are needed to destabilize the MBL phase. At criticality, we find that the entanglement entropy can grow with an exponent 0 < α < 1 anywhere between the area law α = 0 and the volume law α = 1, as a function of the resonances properties, while the entanglement spectrum follows the strong multifractality statistics. In the MBL phase near criticality, we obtain the simple value ν = 1 for the correlation length exponent. Independently of the strong disorder limit, we explain why, for the many-body localization transition concerning individual eigenstates, the correlation length exponent ν is not constrained by the usual Harris inequality ν ≥ 2/d, so that there is no theoretical inconsistency with the best numerical measure ν = 0.8(3) obtained by Luitz et al. (2015).

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“…Intuitively, this is because a partition only disrupts the τ z eigenvalues straddling its boundary. These properties have been used in previous studies to diagnose MBL [12,18,21,65,[72][73][74][75].…”

Section: A the L-bit Ansatzmentioning

confidence: 99%

Many-body localization beyond eigenstates in all dimensions

et al. 2016

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Isolated quantum systems with quenched randomness exhibit many-body localization (MBL), wherein they do not reach local thermal equilibrium even when highly excited above their ground states. It is widely believed that individual eigenstates capture this breakdown of thermalization at finite size. We show that this belief is false in general and that a MBL system can exhibit the eigenstate properties of a thermalizing system. We propose that localized approximately conserved operators (l * -bits) underlie localization in such systems. In dimensions d > 1, we further argue that the existing MBL phenomenology is unstable to boundary effects and gives way to l * -bits. Physical consequences of l * -bits include the possibility of an eigenstate phase transition within the MBL phase unrelated to the dynamical transition in d = 1 and thermal eigenstates at all parameters in d > 1. Near-term experiments in ultra-cold atomic systems and numerics can probe the dynamics generated by boundary layers and emergence of l * -bits.

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Many-body localization transition in Rokhsar-Kivelson-type wave functions

Cited by 23 publications

References 72 publications

Operator entanglement entropy of the time evolution operator in chaotic systems

Operator entanglement entropy of the time evolution operator in chaotic systems

Many-Body-Localization Transition in the Strong Disorder Limit: Entanglement Entropy from the Statistics of Rare Extensive Resonances

Many-body localization beyond eigenstates in all dimensions

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