Traveling/non-traveling phase transition and non-ergodic properties in the random transverse-field Ising model on the Cayley tree

Abstract

We study the random transverse field Ising model on a finite Cayley tree. This enables us to probe key questions arising in other important disordered quantum systems, in particular the Anderson transition and the problem of dirty bosons on the Cayley tree, or the emergence of non-ergodic properties in such systems. We numerically investigate this problem building on the cavity mean-field method complemented by state-of-the art finite-size scaling analysis. Our numerics agree very well with analytical results based on an analogy with the traveling wave problem of a branching random walk in the presence of an absorbing wall. Critical properties and finite-size corrections for the zero-temperature paramagnetic-ferromagnetic transition are studied both for constant and algebraically vanishing boundary conditions. In the later case, we reveal a regime which is reminiscent of the non-ergodic delocalized phase observed in other systems, thus shedding some light on critical issues in the context of disordered quantum systems, such as Anderson transitions, the many-body localization or disordered bosons in infinite dimensions.

References in corpus (92)

• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• Anderson Transitions
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Many-body localization, thermalization, and entanglement
• The many-body localization phase transition
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Phenomenology of fully many-body-localized systems
• Front propagation into unstable states
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• Many-body localization: an introduction and selected topics
• Quasiparticle Lifetime in a Finite System: A Non--Perturbative Approach
• Shift in the velocity of a front due to a cut-off
• Localization of preformed Cooper-pairs in disordered superconductors
• Strong disorder RG approach of random systems
• Recent progress in many-body localization
• Front propagation into unstable states: Universal algebraic convergence towards uniformly translating pulled fronts
• Anderson localization on the Bethe lattice: non-ergodicity of extended states
• Multifractal Scalings across the Many-Body Localization Transition
• A Numerical Study of the Random Transverse-Field Ising Spin Chain
• Emergence of quantum chaos in finite interacting Fermi systems
• A random matrix model with localization and ergodic transitions
• Theoretical Studies of Superconductor-Insulator Transitions
• Anderson localization on random regular graphs
• Non-ergodic phases in strongly disordered random regular graphs
• Scaling theory of the Anderson transition in random graphs: ergodicity and universality
• Many-body localization transition in a lattice model of interacting fermions: statistics of renormalized hoppings in configuration space
• Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity
• Fractality of wave functions on a Cayley tree: Difference between a tree and a locally tree-like graph without boundary
• Rare thermal bubbles at the many-body localization transition from the Fock space point of view
• Non-ergodic delocalized phase in Anderson model on Bethe lattice and regular graph
• From Anderson localization on Random Regular Graphs to Many-Body localization
• Statistics of eigenstates near the localization transition on random regular graphs
• From non-ergodic eigenvectors to local resolvent statistics and back: a random matrix perspective
• Return probability for the Anderson model on the random regular graph
• Superconductor-Insulator transition and energy localization
• Delocalized Glassy Dynamics and Many Body Localization
• The Many-Body localization transition in the Hilbert space
• Infinite disorder scaling of random quantum magnets in three and higher dimensions
• Critical behavior at the localization transition on random regular graphs
• Universal scaling of the order-parameter distribution in strongly disordered superconductors
• Energy transport in strongly disordered superconductors and magnets
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Two critical localization lengths in the Anderson transition on random graphs
• Eigenfunction distribution for the Rosenzweig-Porter model
• Sub-diffusion in the Anderson model on random regular graph
• Multifractality of wave functions on a Cayley tree: From root to leaves
• Fragile ergodic phases in logarithmically-normal Rosenzweig-Porter model
• Criticality and quenched disorder: rare regions vs. Harris criterion
• Anderson model on Bethe lattices: density of states, localization properties and isolated eigenvalue
• Survival probability in Generalized Rosenzweig-Porter random matrix ensemble
• The Lévy-Rosenzweig-Porter random matrix ensemble
• Anderson transition on the Bethe lattice: an approach with real energies
• Multifractality of eigenstates in the delocalized non-ergodic phase of some random matrix models : Wigner-Weisskopf approach
• Non-Ergodic Delocalization in the Rosenzweig-Porter Model
• Multifractality without fine-tuning in a Floquet quasiperiodic chain
• Eigenstate correlations around many-body localization transition
• Critical properties of the Anderson transition in random graphs: two-parameter scaling theory, Kosterlitz-Thouless type flow and many-body localization
• Renormalization group study of random quantum magnets
• Weak Disorder Expansion for the Anderson Model on a Tree
• Non-ergodic delocalized states for efficient population transfer within a narrow band of the energy landscape
• Difference between level statistics, ergodicity and localization transitions on the Bethe lattice
• Anderson localization on the Cayley tree : multifractal statistics of the transmission at criticality and off criticality
• The survival probability of a branching random walk in presence of an absorbing wall
• Universality in Anderson localization on random graphs with varying connectivity
• Anderson transition on the Cayley tree as a traveling wave critical point for various probability distributions
• Level compressibility for the Anderson model on regular random graphs and the eigenvalue statistics in the extended phase
• Anomalous dynamics in the ergodic side of the Many-Body Localization transition and the glassy phase of Directed Polymers in Random Media
• Anderson-Hubbard model with box disorder: Statistical dynamical mean-field theory investigation
• Delocalization and ergodicity of the Anderson model on Bethe lattices
• Bose glass transition and spin-wave localization for 2D bosons in a random potential
• Multifractal states in self-consistent theory of localization: analytical solution
• Exact solution and precise asymptotics of a Fisher-KPP type front
• Hilbert-space fragmentation, multifractality, and many-body localization
• Critical behavior of the Anderson model on the Bethe lattice via a large-deviation approach
• Anderson Localization on the Bethe Lattice using Cages and the Wegner Flow
• The cavity method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media
• Statistics of renormalized on-site energies and renormalized hoppings for Anderson localization models in dimensions d=2 and d=3
• Revisiting classical and quantum disordered systems from the unifying perspective of large deviations
• Anomalous multifractality in quantum chains with strongly correlated disorder
• Localization and chaos in a spin glass model with random fields: Mapping to the localization problem in a Bethe lattice with a correlated disorder
• Random Transverse Field Ising Model in dimension $d>1$ : scaling analysis in the disordered phase from the Directed Polymer model
• Jordan-Wigner transformations for tree structures
• Generating a Fractal Butterfly Floquet Spectrum in a Class of Driven SU(2) Systems: Eigenstate Statistics
• Vanishing corrections for the position in a linear model of FKPP fronts
• Statistics of Green's functions on a disordered Cayley tree and the validity of forward scattering approximation
• Random Transverse Field Ising Model in dimension $d=2,3$ : Infinite Disorder scaling via a non-linear transfer approach
• Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization
• Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
• Random Transverse Field Ising model on the Cayley Tree : analysis via Boundary Strong Disorder Renormalization