Spectral form factor in a minimal bosonic model of many-body quantum chaos

• URL: http://arxiv.org/abs/2203.05439v2
• Date: Mon, 29 Aug 2022 15:31:05 GMT
• Title: Spectral form factor in a minimal bosonic model of many-body quantum chaos
• Authors: Dibyendu Roy, Divij Mishra and Toma\v{z} Prosen
• Abstract summary: We study spectral form factor in periodically-kicked bosonic chains. We numerically find a nontrivial systematic system-size dependence of the Thouless time.
• Score: 1.3793594968500609
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study spectral form factor in periodically-kicked bosonic chains. We consider a family of models where a Hamiltonian with the terms diagonal in the Fock space basis, including random chemical potentials and pair-wise interactions, is kicked periodically by another Hamiltonian with nearest-neighbor hopping and pairing terms. We show that for intermediate-range interactions, random phase approximation can be used to rewrite the spectral form factor in terms of a bi-stochastic many-body process generated by an effective bosonic Hamiltonian. In the particle-number conserving case, i.e., when pairing terms are absent, the effective Hamiltonian has a non-abelian $SU(1,1)$ symmetry, resulting in universal quadratic scaling of the Thouless time with the system size, irrespective of the particle number. This is a consequence of degenerate symmetry multiplets of the subleading eigenvalue of the effective Hamiltonian and is broken by the pairing terms. In the latter case, we numerically find a nontrivial systematic system-size dependence of the Thouless time, in contrast to a related recent study for kicked fermionic chains.

Related papers

• Interacting chiral fermions on the lattice with matrix product operator norms [37.69303106863453]
  We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice. The fermion doubling problem is circumvented by constructing a Fock space endowed with a semi-definite norm. We demonstrate that the scaling limit of the free model recovers the chiral fermion field.
  arXiv  Detail & Related papers  (2024-05-16T17:46:12Z)
• Entanglement Hamiltonian for inhomogeneous free fermions [0.0]
  We study the entanglement Hamiltonian for the ground state of one-dimensional free fermions in the presence of an inhomogeneous chemical potential. It is shown that, for both models, conformal field theory predicts a Bisognano-Wichmann form for the entangement Hamiltonian of a half-infinite system.
  arXiv  Detail & Related papers  (2024-03-21T18:13:10Z)
• Entangled Collective Spin States of Two Species Ultracold atoms in a Ring [0.0]
  We study the general quantum Hamiltonian that can be realized with two species of degenerate ultracold atoms in a ring-shaped trap. We examine the spectrum and the states with a collective spin picture in a Dicke state basis. The density of states for the full Hamiltonian shows features as of phase transition in varying between linear and quadratic limits.
  arXiv  Detail & Related papers  (2023-03-15T04:11:59Z)
• Entropy decay for Davies semigroups of a one dimensional quantum lattice [13.349045680843885]
  We show that the relative entropy between any evolved state and the equilibrium Gibbs state contracts exponentially fast with an exponent that scales logarithmically with the length of the chain. This has wide-ranging applications to the study of many-body in and out-of-equilibrium quantum systems.
  arXiv  Detail & Related papers  (2021-12-01T16:15:58Z)
• Fragility to quantum fluctuations of classical Hamiltonian period doubling [0.0]
  We add quantum fluctuations to a classical period-doubling Hamiltonian time crystal, replacing the $N$ classical interacting angular momenta with quantum spins of size $l$. The full permutation symmetry of the Hamiltonian allows a mapping to a bosonic model and the application of exact diagonalization for quite large system size.
  arXiv  Detail & Related papers  (2021-08-25T18:02:57Z)
• Linear growth of the entanglement entropy for quadratic Hamiltonians and arbitrary initial states [11.04121146441257]
  We prove that the entanglement entropy of any pure initial state of a bosonic quantum system grows linearly in time. We discuss several applications of our results to physical systems with (weakly) interacting Hamiltonians and periodically driven quantum systems.
  arXiv  Detail & Related papers  (2021-07-23T07:55:38Z)
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
  We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-20T18:44:06Z)
• Qubit regularization of asymptotic freedom [35.37983668316551]
  Heisenberg-comb acts on a Hilbert space with only two qubits per spatial lattice site. We show that the model reproduces the universal step-scaling function of the traditional model up to correlation lengths of 200,000 in lattice units. We argue that near-term quantum computers may suffice to demonstrate freedom.
  arXiv  Detail & Related papers  (2020-12-03T18:41:07Z)
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions [1.2433211248720717]
  The concept of out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness. We define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. We demonstrate an equivalent formalism of computation using a general time independent Hamiltonian.
  arXiv  Detail & Related papers  (2020-08-06T07:53:28Z)
• 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)
• Random Matrix Spectral Form Factor in Kicked Interacting Fermionic Chains [1.6295305195753724]
  We study quantum chaos and spectral correlations in periodically driven (Floquet) fermionic chains with long-range two-particle interactions. We analytically show that the spectral form factor precisely follows the prediction of random matrix theory in the regime of long chains.
  arXiv  Detail & Related papers  (2020-05-21T07:02:04Z)

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.