Chaos in the Bose-Hubbard model and random two-body Hamiltonians

• URL: http://arxiv.org/abs/2109.06236v2
• Date: Mon, 10 Jan 2022 13:40:10 GMT
• Title: Chaos in the Bose-Hubbard model and random two-body Hamiltonians
• Authors: Lukas Pausch, Edoardo G. Carnio, Andreas Buchleitner, Alberto Rodr\'iguez
• Abstract summary: 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.
• Score: 6.528382036284375
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the chaotic phase of the Bose-Hubbard model [L. Pausch et al, Phys. Rev. Lett. 126, 150601 (2021)] in relation to the bosonic embedded random matrix ensemble, which mirrors the dominant few-body nature of many-particle interactions, and hence the Fock space sparsity of quantum many-body systems. The energy dependence of the chaotic regime is well described by the bosonic embedded ensemble, which also reproduces the Bose-Hubbard chaotic eigenvector features, quantified by the expectation value and eigenstate-to-eigenstate fluctuations of fractal dimensions. Despite this agreement, in terms of the fractal dimension distribution, these two models depart from each other and from the Gaussian orthogonal ensemble as Hilbert space grows. These results provide further evidence of a way to discriminate among different many-body Hamiltonians in the chaotic regime.

Related papers

• Topological quantum slinky motion in resonant extended Bose-Hubbard model [0.0]
  We study the one-dimensional Bose-Hubbard model under the resonant condition. A series of quantum slinky oscillations occur in a two-site system for boson numbers $nin lbrack 2,infty )$.
  arXiv  Detail & Related papers  (2024-10-17T06:20:09Z)
• Quantum Chaos on Edge [36.136619420474766]
  We identify two different classes: the near edge physics of sparse'' and the near edge of dense'' chaotic systems. The distinction lies in the ratio between the number of a system's random parameters and its Hilbert space dimension. While the two families share identical spectral correlations at energy scales comparable to the level spacing, the density of states and its fluctuations near the edge are different.
  arXiv  Detail & Related papers  (2024-03-20T11:31:51Z)
• Universal correlations in chaotic many-body quantum states: Fock-space formulation of Berrys random wave model [0.0]
  We show that the randomness of chaotic eigenstates in interacting quantum systems hides subtle correlations imposed by their finite energy per particle. These correlations are revealed when Berrys approach for chaotic eigenfunctions in single-particle systems is lifted into many-body space. We then identify the universality of both the cross-correlations and the Gaussian distribution of expansion coefficients as the signatures of chaotic eigenstates.
  arXiv  Detail & Related papers  (2024-03-15T09:26:17Z)
• Quantized Thouless pumps protected by interactions in dimerized Rydberg tweezer arrays [41.94295877935867]
  In the noninteracting case, quantized Thouless pumps can only occur when a topological singularity is encircled adiabatically. In the presence of interactions, such topological transport can even persist for exotic paths in which the system gets arbitrarily close to the noninteracting singularity.
  arXiv  Detail & Related papers  (2024-02-14T16:58:21Z)
• Exotic quantum liquids in Bose-Hubbard models with spatially-modulated symmetries [0.0]
  We investigate the effect that spatially modulated continuous conserved quantities can have on quantum ground states. We show that such systems feature a non-trivial Hilbert space fragmentation for momenta incommensurate with the lattice. We conjecture that a Berezinskii-Kosterlitz-Thouless-type transition is driven by the unbinding of vortices along the temporal direction.
  arXiv  Detail & Related papers  (2023-07-17T18:14:54Z)
• 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)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Hilbert Space Fragmentation and Exact Scars of Generalized Fredkin Spin Chains [0.0]
  We introduce a family of spin-$1/2$ many-body Hamiltonians with a three-site interaction. The interplay between fragmentation and scarring leads to rich tunable non-ergodic dynamics.
  arXiv  Detail & Related papers  (2021-02-11T16:45:17Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• 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)

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.