Eigenstate entanglement in integrable collective spin models

• URL: http://arxiv.org/abs/2108.09866v3
• Date: Mon, 25 Apr 2022 21:36:54 GMT
• Title: Eigenstate entanglement in integrable collective spin models
• Authors: Meenu Kumari, \'Alvaro M. Alhambra
• Abstract summary: The average entanglement entropy (EE) of the energy eigenstates in non-vanishing partitions has been recently proposed as a diagnostic of integrability in quantum many-body systems. We numerically demonstrate that the aforementioned average EE in the thermodynamic limit is universal for all parameter values of the LMG model.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The average entanglement entropy (EE) of the energy eigenstates in non-vanishing partitions has been recently proposed as a diagnostic of integrability in quantum many-body systems. For it to be a faithful characterization of quantum integrability, it should distinguish quantum systems with a well-defined classical limit in the same way as the unequivocal classical integrability criteria. We examine the proposed diagnostic in the class of collective spin models characterized by permutation symmetry in the spins. The well-known Lipkin-Meshov-Glick (LMG) model is a paradigmatic integrable system in this class with a well-defined classical limit. Thus, this model is an excellent testbed for examining quantum integrability diagnostics. First, we calculate analytically the average EE of the Dicke basis $\{|j,m\rangle \}_{m=-j}^j$ in any non-vanishing bipartition, and show that in the thermodynamic limit, it converges to $1/2$ of the maximal EE in the corresponding bipartition. Using finite-size scaling, we numerically demonstrate that the aforementioned average EE in the thermodynamic limit is universal for all parameter values of the LMG model. Our analysis illustrates how a value of the average EE far away from the maximal in the thermodynamic limit could be a signature of integrability.

Related papers

• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model [0.0]
  We study the average and the standard deviation of the entanglement entropy of highly excited eigenstates of the integrable interacting spin-$frac12$ XYZ chain. We find that the average eigenstate entanglement entropy exhibits a volume-law coefficient that is smaller than that universally of quantum-chaotic interacting models.
  arXiv  Detail & Related papers  (2023-11-17T19:00:09Z)
• Spectral chaos bounds from scaling theory of maximally efficient quantum-dynamical scrambling [49.1574468325115]
  A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient. We develop a single- parameter scaling theory for the spectral statistics in this scenario, which embodies exact self-similarity of the spectral correlations along the complete scrambling dynamics. We establish that scaling predictions are matched by a privileged process, and serve as bounds for other dynamical scrambling scenarios, allowing one to quantify inefficient or incomplete scrambling on all timescales.
  arXiv  Detail & Related papers  (2023-10-17T15:41:50Z)
• Universal properties of dissipative Tomonaga-Luttinger liquids: Case study of a non-Hermitian XXZ spin chain [3.4253416336476246]
  We demonstrate the universal properties of dissipative Tomonaga-Luttinger (TL) liquids by calculating correlation functions and performing finite-size scaling analysis. Our results can be tested with the two-component Bose-Hubbard system of ultracold atoms subject to two-body loss.
  arXiv  Detail & Related papers  (2021-12-23T11:16:31Z)
• Entanglement dynamics of thermofield double states in integrable models [0.0]
  We study the entanglement dynamics of thermofield double (TFD) states in integrable spin chains and quantum field theories. We show that, for a natural choice of the Hamiltonian eigenbasis, the TFD evolution may be interpreted as a quantum quench from an initial state. We conjecture a formula for the entanglement dynamics, which is valid for both discrete and continuous integrable field theories.
  arXiv  Detail & Related papers  (2021-12-03T16:40:36Z)
• Eigenstate capacity and Page curve in fermionic Gaussian states [0.0]
  Capacity of entanglement (CoE) is an information-theoretic measure of entanglement, defined as the variance of modular Hamiltonian. We derive an exact expression for the average eigenstate CoE in fermionic Gaussian states as a finite series. We identify this as a distinguishing feature between integrable and quantum-chaotic systems.
  arXiv  Detail & Related papers  (2021-09-01T18:00:10Z)
• On the properties of the asymptotic incompatibility measure in multiparameter quantum estimation [62.997667081978825]
  Incompatibility (AI) is a measure which quantifies the difference between the Holevo and the SLD scalar bounds. We show that the maximum amount of AI is attainable only for quantum statistical models characterized by a purity larger than $mu_sf min = 1/(d-1)$.
  arXiv  Detail & Related papers  (2021-07-28T15:16:37Z)
• Uhlmann Fidelity and Fidelity Susceptibility for Integrable Spin Chains at Finite Temperature: Exact Results [68.8204255655161]
  We show that the proper inclusion of the odd parity subspace leads to the enhancement of maximal fidelity susceptibility in the intermediate range of temperatures. The correct low-temperature behavior is captured by an approximation involving the two lowest many-body energy eigenstates.
  arXiv  Detail & Related papers  (2021-05-11T14:08:02Z)
• Exact thermal properties of free-fermionic spin chains [68.8204255655161]
  We focus on spin chain models that admit a description in terms of free fermions. Errors stemming from the ubiquitous approximation are identified in the neighborhood of the critical point at low temperatures.
  arXiv  Detail & Related papers  (2021-03-30T13:15:44Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature [62.997667081978825]
  We present a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction.
  arXiv  Detail & Related papers  (2021-01-21T14:33:34Z)
• Long-range level correlations in quantum systems with finite Hilbert space dimension [0.0]
  We study the spectral statistics of quantum systems with finite Hilbert spaces. We derive a theorem showing that eigenlevels in such systems cannot be globally uncorrelated.
  arXiv  Detail & Related papers  (2020-10-13T15:49:15Z)

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.