The cavity method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media

Abstract

After reviewing the basics of the cavity method in classical systems, we show how its quantum version, with some appropriate approximation scheme, can be used to study a system of spins with random ferromagnetic interactions and a random transverse field. The quantum cavity equations describing the ferromagnetic-paramagnetic phase transition can be transformed into the well-known problem of a classical directed polymer in a random medium. The glass transition of this polymer problem translates ino the existence of a `Griffith phase' close to the quantum phase transition of the quantum spin problem, where the physics is dominated by rare events.

References in corpus (6)

• Broken Replica Symmetry Bounds in the Mean Field Spin Glass Model
• Renormalization group study of the two-dimensional random transverse-field Ising model
• Superconductor-Insulator transition and energy localization
• Entanglement Entropy in the Two-Dimensional Random Transverse Field Ising Model
• 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

Cited by in corpus (23)

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• The performance of the quantum adiabatic algorithm on random instances of two optimization problems on regular hypergraphs
• Strong Disorder RG approach - a short review of recent developments
• Infinite disorder scaling of random quantum magnets in three and higher dimensions
• Universal scaling of the order-parameter distribution in strongly disordered superconductors
• Enhancement of Tc in the Superconductor-Insulator Phase Transition on Scale-Free Networks
• Revisiting classical and quantum disordered systems from the unifying perspective of large deviations
• Real-space renormalization-group approach to the random transverse-field Ising model in finite dimensions
• Random Transverse Field Ising Model in dimension $d>1$ : scaling analysis in the disordered phase from the Directed Polymer model
• Random Transverse Field Ising Model in dimension $d=2,3$ : Infinite Disorder scaling via a non-linear transfer approach
• Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
• Random Transverse Field Spin-Glass Model on the Cayley tree : phase transition between the two Many-Body-Localized Phases
• Random Transverse Field Ising model on the Cayley Tree : analysis via Boundary Strong Disorder Renormalization
• Low-temperature excitations within the Bethe approximation
• Quantum Cluster Variational Method and Message Passing Algorithms Revisited
• Finite-size scaling analysis of the two-dimensional random transverse-field Ising ferromagnet
• Bethe free-energy approximations for disordered quantum systems
• Dynamical barriers for the random ferromagnetic Ising model on the Cayley tree : traveling-wave solution of the real space renormalization flow
• Random geometry at an infinite-randomness fixed point
• Boundary critical phenomena of the random transverse Ising model in D>=2 dimensions
• Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree
• Efficient inference in the transverse field Ising model
• Large deviations in the many-body localization transition: The case of the random-field XXZ chain