Chaos and ergodicity across the energy spectrum of interacting bosons

• URL: http://arxiv.org/abs/2009.05295v2
• Date: Wed, 20 Jan 2021 16:53:14 GMT
• Title: Chaos and ergodicity across the energy spectrum of interacting bosons
• Authors: Lukas Pausch, Edoardo G. Carnio, Alberto Rodr\'iguez, Andreas Buchleitner
• Abstract summary: 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.
• Score: 6.528382036284375
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

Related papers

• Bounding multifractality by observables [0.0]
  Fractal dimensions have been used as a measure for structure of eigenstates of quantum many-body systems. We discuss how this structure of the observables can be used to bound the fractal dimensions from above. We then consider how such upper bounds act as a proxy for the fractal dimension over the many-body localization transition.
  arXiv  Detail & Related papers  (2025-01-29T13:29:20Z)
• Tensor product random matrix theory [39.58317527488534]
  We introduce a real-time field theory approach to the evolution of correlated quantum systems. We describe the full range of such crossover dynamics, from initial product states to a maximum entropy ergodic state.
  arXiv  Detail & Related papers  (2024-04-16T21:40:57Z)
• Entanglement Fractalization [9.254741613227333]
  We numerically explore the interplay of fractal geometry and quantum entanglement by analyzing entanglement entropy and the entanglement contour in the scaling limit. For gapless ground states exhibiting a finite density of states at the chemical potential, we reveal a super-area law. A novel self-similar and universal pattern termed an entanglement fractal'' in the entanglement contour data as we approach the scaling limit bears resemblance to intricate Chinese paper-cutting designs.
  arXiv  Detail & Related papers  (2023-11-02T12:50:27Z)
• Matter relative to quantum hypersurfaces [44.99833362998488]
  We extend the Page-Wootters formalism to quantum field theory. By treating hypersurfaces as quantum reference frames, we extend quantum frame transformations to changes between classical and nonclassical hypersurfaces.
  arXiv  Detail & Related papers  (2023-08-24T16:39:00Z)
• Chaos and bi-partite entanglement between Bose-Joephson junctions [0.0]
  The entanglement between two bosonic Josephson junctions is studied in relation to the classical mixed phasespace structure of the system. The symmetry-resolved entanglement spectrum and bi-partite entanglement entropy of the system's energy eigenstates are calculated.
  arXiv  Detail & Related papers  (2022-08-17T09:59:44Z)
• Nonperturbative Casimir effects: Vacuum structure, Confinement, and Chiral Symmetry Breaking [91.3755431537592]
  We consider phase properties of confining gauge theories and strongly interacting fermion systems. In particular, the chiral and deconfinement phase transitions properties in the presence of Casimir plates.
  arXiv  Detail & Related papers  (2022-08-06T07:39:36Z)
• Multifractality in quasienergy space of coherent states as a signature of quantum chaos [8.402742655847774]
  We show the manifestation of phase space structures in the multifractal properties of coherent states. By tuning the kicking strength, the system undergoes a transition from regularity to chaos. The onset of chaos is clearly identified by the phase space averaged multifractal dimensions.
  arXiv  Detail & Related papers  (2021-10-20T11:42:49Z)
• Chaos in the Bose-Hubbard model and random two-body Hamiltonians [6.528382036284375]
  We investigate the chaotic phase of the Bose-Hubbard model in relation to the bosonic embedded random matrix ensemble. Results provide further evidence of a way to discriminate among different many-body Hamiltonians in the chaotic regime.
  arXiv  Detail & Related papers  (2021-09-13T18:12:59Z)
• Emergence of classical behavior in the early universe [68.8204255655161]
  Three notions are often assumed to be essentially equivalent, representing different facets of the same phenomenon. We analyze them in general Friedmann-Lemaitre- Robertson-Walker space-times through the lens of geometric structures on the classical phase space. The analysis shows that: (i) inflation does not play an essential role; classical behavior can emerge much more generally; (ii) the three notions are conceptually distinct; classicality can emerge in one sense but not in another.
  arXiv  Detail & Related papers  (2020-04-22T16:38:25Z)
• Dynamical solitons and boson fractionalization in cold-atom topological insulators [110.83289076967895]
  We study the $mathbbZ$ Bose-Hubbard model at incommensurate densities. We show how defects in the $mathbbZ$ field can appear in the ground state, connecting different sectors. Using a pumping argument, we show that it survives also for finite interactions.
  arXiv  Detail & Related papers  (2020-03-24T17:31:34Z)
• Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
  We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
  arXiv  Detail & Related papers  (2020-03-16T11:37:23Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.