Optimal route to quantum chaos in the Bose-Hubbard model

Abstract

The dependence of the chaotic phase of the Bose-Hubbard Hamiltonian on particle number $N$, system size $L$ and particle density is investigated in terms of spectral and eigenstate features. We analyze the development of the chaotic phase as the limit of infinite Hilbert space dimension is approached along different directions, and show that the fastest route to chaos is the path at fixed density $n\lesssim 1$. The limit $N\to \infty$ at constant $L$ leads to a slower convergence of the chaotic phase towards the random matrix theory benchmarks. In this case, from the distribution of the eigenstate generalized fractal dimensions, the ergodic phase becomes more distinguishable from random matrix theory for larger $N$, in a similar way as along trajectories at fixed density.

9 pages, 8 figures

References in corpus (19)

• Many-Body Physics with Ultracold Gases
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Localization of interacting fermions at high temperature
• 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
• Semiclassical Foundation of Universality in Quantum Chaos
• Off-diagonal matrix elements of local operators in many-body quantum systems
• Critical parameters from generalised multifractal analysis at the Anderson transition
• Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit
• Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined
• Extended nonergodic states in disordered many-body quantum systems
• 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
• Complexity in parametric Bose-Hubbard Hamiltonians and structural analysis of eigenstates
• Wavepacket dynamics in energy space of a chaotic trimeric Bose-Hubbard system
• Chaos in the Bose-Hubbard model and random two-body Hamiltonians
• Many-body interference in bosonic dynamics

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