Many-body Localization Transition in Rokhsar-Kivelson-type wave functions

Abstract

We construct a family of many-body wave functions to study the many-body localization phase transition. The wave functions have a Rokhsar-Kivelson form, in which the weight for the configurations are chosen from the Gibbs weights of a classical spin glass model, known as the Random Energy Model, multiplied by a random sign structure to represent a highly excited state. These wave functions show a phase transition into an MBL phase. In addition, we see three regimes of entanglement scaling with subsystem size: scaling with entanglement corresponding to an infinite temperature thermal phase, constant scaling, and a sub-extensive scaling between these limits. Near the phase transition point, the fluctuations of the Rényi entropies are non-Gaussian. We find that Rényi entropies with different Rényi index transition into the MBL phase at different points and have different scaling behavior, suggesting a multifractal behavior.

Published version. Improved version with 1 new references; 17 pages, 68 references and 16 figures 9some have been reordered)

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Cited by in corpus (20)

• Quantum Zeno Effect and the Many-body Entanglement Transition
• Anomalous thermalization in ergodic systems
• Long tail distributions near the many body localization transition
• Operator entanglement entropy of the time evolution operator in chaotic systems
• Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge
• Nature of Many-Body Localization and Transitions by Density Matrix Renormaliztion Group and Exact Diagonalization Studies
• Bimodal entanglement entropy distribution in the many-body localization transition
• Many-body localization beyond eigenstates in all dimensions
• Many-Body Localization in Spin Chain Systems with Quasiperiodic Fields
• The many-body localized phase of the quantum random energy model
• A model for continuous thermal Metal to Insulator Transition
• Non-ergodic delocalized phase with Poisson level statistics
• Many-Body-Localization Transition : strong multifractality spectrum for matrix elements of local operators
• Classical Glasses, Black Holes, and Strange Quantum Liquids
• Many Body Localization Transition in the strong disorder limit : entanglement entropy from the statistics of rare extensive resonances
• Disorder perturbed Flat Bands II: a search for criticality
• Statistical properties of the Green function in finite size for Anderson Localization models with multifractal eigenvectors
• Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
• Entanglement transitions from restricted Boltzmann machines
• Kosterlitz-Thouless phase and $Z_d$ topological quantum phase