Nonergodic dynamics of the one-dimensional Bose-Hubbard model with a trapping potential
arXiv:2108.01238 · doi:10.1103/PhysRevA.104.043322
Abstract
We investigate nonergodic behavior of the one-dimensional Bose-Hubbard model, which emerges in the unitary quantum dynamics starting with initial-state in the presence of a trapping potential. We compute the level spacing statistic, the time evolution of the number imbalance between the odd and the even sites, and the entanglement entropy in order to show that the system exhibits nonergodicity in a strongly interacting regime. The trapping potential enhances nonergodicity even when the trapping potential is weak compared to the the hopping energy. We derive the effective spin-1/2 {\it XXZ} Hamiltonian for the strongly interacting regimes by using a perturbation method. On the basis of the effective Hamiltonian, we show that the trapping potential is effectively strengthened by the on-site interaction, leading to the enhancement of the nonergodic behavior. We also calculate the real-time dynamics under the effective Hamiltonian and find that the entanglement entropy grows logarithmically in time.
10 pages, 10 figures
References in corpus (17)
- Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
- Thermalization and its mechanism for generic isolated quantum systems
- Probing many-body dynamics on a 51-atom quantum simulator
- Many body localization and thermalization in quantum statistical mechanics
- Localization of interacting fermions at high temperature
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Phenomenology of fully many-body-localized systems
- Breakdown of thermalization in finite one-dimensional systems
- Controlling many-body dynamics with driven quantum scars in Rydberg atom arrays
- Generalized Thermalization in an Integrable Lattice System
- Relaxation and thermalization in the one-dimensional Bose-Hubbard model: A case study for the interaction quantum quench from the atomic limit
- Many-body localization due to random interactions
- Statistical properties of the spectrum the extended Bose-Hubbard model
- Spin dynamics for bosons in an optical lattice
- Many-body localization of bosons in optical lattice: Dynamics in disorder-free potentials
- Many-body localization for randomly interacting bosons
- Guide to Exact Diagonalization Study of Quantum Thermalization