On the quantum spin glass transition on the Bethe lattice

Abstract

We investigate the ground-state properties of a disorderd Ising model with uniform transverse field on the Bethe lattice, focusing on the quantum phase transition from a paramagnetic to a glassy phase that is induced by reducing the intensity of the transverse field. We use a combination of quantum Monte Carlo algorithms and exact diagonalization to compute Rényi entropies, quantum Fisher information, correlation functions and order parameter. We locate the transition by means of the peak of the Rényi entropy and we find agreement with the transition point estimated from the emergence of finite values of the Edwards-Anderson order parameter and from the peak of the correlation length. We interpret the results by means of a mean-field theory in which quantum fluctuations are treated as massive particles hopping on the interaction graph. We see that the particles are delocalized at the transition, a fact that points towards the existence of possibly another transition deep in the glassy phase where these particles localize, therefore leading to a many-body localized phase.

18 pages, 17 figures

References in corpus (19)

• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Integrals of motion in the Many-Body localized phase
• Constructing local integrals of motion in the many-body localized phase
• Ergodicity breaking in a model showing many-body localization
• How Powerful is Adiabatic Quantum Computation?
• Many-body mobility edge in a mean-field quantum spin glass
• Entanglement Entropy and Twist Fields
• Size dependence of the minimum excitation gap in the Quantum Adiabatic Algorithm
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Measures of macroscopicity for quantum spin systems
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
• Finite Size Scaling of Mutual Information: A Scalable Simulation
• On the path integral representation for quantum spin models and its application to the quantum cavity method and to Monte Carlo simulations
• Cavity method for quantum spin glasses on the Bethe lattice
• Quantum annealing: the fastest route to quantum computation?
• Quantum and Classical in Adiabatic Computation

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