Exact solution of a percolation analogue for the many-body localisation transition

Abstract

We construct and solve a classical percolation model with a phase transition that we argue acts as a proxy for the quantum many-body localisation transition. The classical model is defined on a graph in the Fock space of a disordered, interacting quantum spin chain, using a convenient choice of basis. Edges of the graph represent matrix elements of the spin Hamiltonian between pairs of basis states that are expected to hybridise strongly. At weak disorder, all nodes are connected, forming a single cluster. Many separate clusters appear above a critical disorder strength, each typically having a size that is exponentially large in the number of spins but a vanishing fraction of the Fock-space dimension. We formulate a transfer matrix approach that yields an exact value $\nu =2$ for the localisation length exponent, and also use complete enumeration of clusters to study the transition numerically in finite-sized systems.

arXiv comment5 pages, 4 figures + supplementary material

References in corpus (24)

• Many body localization and thermalization in quantum statistical mechanics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Localization of interacting fermions at high temperature
• The many-body localization phase transition
• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Interacting electrons in disordered wires: Anderson localization and low-temperature transport
• Glassy dynamics of kinetically constrained models
• On Many-Body Localization for Quantum Spin Chains
• Many-body localization in a disordered quantum Ising chain
• Dynamic first-order phase transition in kinetically constrained models of glasses
• Theory of the many-body localization transition in one dimensional systems
• Universal properties of many-body delocalization transitions
• Ergodicity breaking in a model showing many-body localization
• Critical Properties of the Many-Body Localization Transition
• Analytically solvable renormalization group for the many-body localization transition
• Kosterlitz-Thouless scaling at many-body localization phase transitions
• Long tail distributions near the many body localization transition
• Scaling Theory of Entanglement at the Many-Body Localization Transition
• The many-body localized phase of the quantum random energy model
• Many-body localization in Fock-space: a local perspective
• A semi-classical limit for the many-body localization transition
• Percolation in Fock space as a proxy for many-body localisation
• Simple probability distributions on a Fock-space lattice

Cited by in corpus (26)

• Multifractal Scalings across the Many-Body Localization Transition
• Rare thermal bubbles at the many-body localization transition from the Fock space point of view
• The Many-Body localization transition in the Hilbert space
• Dynamical phases in a "multifractal" Rosenzweig-Porter model
• Sub-diffusion in the Anderson model on random regular graph
• Fock-space correlations and the origins of many-body localisation
• Chain breaking and Kosterlitz-Thouless scaling at the many-body localization transition in the random field Heisenberg spin chain
• Percolation in Fock space as a proxy for many-body localisation
• Fock-space anatomy of eigenstates across the many-body localisation transition
• Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions
• Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs
• Localisation on certain graphs with strongly correlated disorder
• Strong ergodicity breaking due to local constraints in a quantum system
• Entanglement in non-equilibrium steady states and many-body localization breakdown in a current driven system
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Many-body localization as a percolation phenomenon
• The Fock-space landscape of many-body localisation
• Probability transport on the Fock space of a disordered quantum spin chain
• Structural properties of local integrals of motion across the many-body localization transition via a fast and efficient method for their construction
• Localization in the constrained quantum annealing of graph coloring
• Localization crossover and subdiffusive transport in a classical facilitated network model of a disordered, interacting quantum spin chain
• Anatomy of localisation protected quantum order on Hilbert space
• Analog charged black hole formation via percolation: Exploring cosmic censorship and Hoop conjecture
• Heat percolation in many-body flatband localizing systems
• Information Bounds on phase transitions in disordered systems
• Orthogonal projections of hypercubes