Chaos and ergodicity across the energy spectrum of interacting bosons

Abstract

We identify the chaotic phase of the Bose-Hubbard Hamiltonian by the energy-resolved correlation between spectral features and structural changes of the associated eigenstates as exposed by their generalized fractal dimensions. The eigenvectors are shown to become ergodic in the thermodynamic limit, in the configuration space Fock basis, in which random matrix theory offers a remarkable description of their typical structure. The distributions of the generalized fractal dimensions, however, are ever more distinguishable from random matrix theory as the Hilbert space dimension grows.

4 pages, 4 figures + supplemental material

References in corpus (22)

• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Localization of interacting fermions at high temperature
• Single-Atom Resolved Fluorescence Imaging of an Atomic Mott Insulator
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Strongly Correlated Quantum Walks in Optical Lattices
• Off-diagonal matrix elements of local operators in many-body quantum systems
• Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit
• Zero-Transmission Law for Multiport Beam Splitters
• Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy
• Statistical properties of the spectrum the extended Bose-Hubbard model
• Nearest-Neighbor Detection of Atoms in a 1D Optical Lattice by Fluorescence Imaging
• Rényi entropy of a line in two-dimensional Ising models
• Experimental statistical signature of many-body quantum interference
• Probing symmetries of quantum many-body systems through gap ratio statistics
• Multifractality meets entanglement: relation for non-ergodic extended states
• Multifractality and its role in anomalous transport in the disordered XXZ spin-chain
• Complexity in parametric Bose-Hubbard Hamiltonians and structural analysis of eigenstates
• Wavepacket dynamics in energy space of a chaotic trimeric Bose-Hubbard system
• Extracting the field theory description of a quantum many-body system from experimental data
• High values of disorder-generated multifractals and logarithmically correlated processes

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