Symmetry Resolved Entanglement with $U(1)$ Symmetry: Some Closed Formulae for Excited States

• URL: http://arxiv.org/abs/2504.08668v1
• Date: Fri, 11 Apr 2025 16:20:29 GMT
• Title: Symmetry Resolved Entanglement with $U(1)$ Symmetry: Some Closed Formulae for Excited States
• Authors: Olalla A. Castro-Alvaredo, Lucía Santamaría-Sanz,
• Abstract summary: We write general formulae for the entropies of excited states consisting of an arbitrary number of subsets of identical excitations.<n>For qubit states consisting of particles of the same charge, the symmetry entropies are independent of region size relative to system size.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this work, we revisit a problem we addressed in previous publications with various collaborators, that is, the computation of the symmetry resolved entanglement entropies of zero-density excited states in infinite volume. The universal nature of the charged moments of these states has already been noted previously. Here, we investigate this problem further, by writing general formulae for the entropies of excited states consisting of an arbitrary number of subsets of identical excitations. When the initial state is written in terms of qubits with appropriate probabilistic coefficients, we find the final formulae to be of a combinatorial nature too. We analyse some of their features numerically and analytically and find that for qubit states consisting of particles of the same charge, the symmetry resolved entropies are independent of region size relative to system size, even if the number and configuration entropies are not.

Related papers

• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices [37.69303106863453]
  Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by unitary dynamics and dissipation. We show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue. We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model.
  arXiv  Detail & Related papers  (2025-04-11T14:06:05Z)
• Symmetry breaking in chaotic many-body quantum systems at finite temperature [0.0]
  Recent work has shown that the entanglement of finite-temperature eigenstates in chaotic quantum many-body local Hamiltonians can be accurately described.<n>We build upon this result to investigate the universal symmetry-breaking properties of such eigenstates.
  arXiv  Detail & Related papers  (2025-04-08T15:41:54Z)
• Symmetry-Resolved Relative Entropy of Random States [0.0]
  We calculate the relative entropy of symmetric random states drawn from the Wishart ensemble.<n>Our findings reveal that the symmetry-resolved relative entropy of random pure states displays universal statistical behavior.
  arXiv  Detail & Related papers  (2024-11-03T09:16:24Z)
• Non-equilibrium dynamics of charged dual-unitary circuits [44.99833362998488]
  interplay between symmetries and entanglement in out-of-equilibrium quantum systems is currently at the centre of an intense multidisciplinary research effort. We show that one can introduce a class of solvable states, which extends that of generic dual unitary circuits. In contrast to the known class of solvable states, which relax to the infinite temperature state, these states relax to a family of non-trivial generalised Gibbs ensembles.
  arXiv  Detail & Related papers  (2024-07-31T17:57:14Z)
• Unraveling the emergence of quantum state designs in systems with symmetry [15.699822139827916]
  We study the emergence of state designs from the random generator states exhibiting symmetries. We find faster convergence of the trace distance during the early time evolution in comparison to the cases when the symmetry is broken. We expect our findings to pave the way for further exploration of deep thermalization and equilibration of closed and open quantum many-body systems.
  arXiv  Detail & Related papers  (2024-02-14T05:35:03Z)
• Asymmetry activation and its relation to coherence under permutation operation [53.64687146666141]
  A Dicke state and its decohered state are invariant for permutation. When another qubits state to each of them is attached, the whole state is not invariant for permutation, and has a certain asymmetry for permutation.
  arXiv  Detail & Related papers  (2023-11-17T03:33:40Z)
• Asymptotic Equipartition Theorems in von Neumann algebras [16.37352624912904]
  We show that the smooth max entropy of i.i.d. states on a von Neumann algebra has an rate given by the quantum relative entropy. Our AEP not only applies to states, but also to quantum channels with appropriate restrictions.
  arXiv  Detail & Related papers  (2022-12-30T13:42:35Z)
• Symmetry-resolved Page curves [0.0]
  We study a natural extension in the presence of a conservation law and introduce the symmetry-resolved Page curves. We derive explicit analytic formulae for two important statistical ensembles with a $U(1)$-symmetry.
  arXiv  Detail & Related papers  (2022-06-10T13:22:14Z)
• Symmetry Resolved Entanglement of Excited States in Quantum Field Theory I: Free Theories, Twist Fields and Qubits [0.0]
  We study the entanglement content of such zero-density excited states focusing on the symmetry resolved entanglement. The ratio of charged moments between the excited and grounds states, from which the symmetry resolved entanglement entropy can be obtained, takes a very simple and universal form. Using form factor techniques, we obtain both the ratio of moments and the symmetry resolved entanglement entropies in complex free theories which possess $U(1)$ symmetry.
  arXiv  Detail & Related papers  (2022-03-23T17:15:44Z)
• Finite-size corrections in critical symmetry-resolved entanglement [0.0]
  We show that the nature of the symmetry group plays a crucial role in symmetry-resolved entanglement entropies. In the case of a discrete symmetry group, the corrections decay algebraically with system size, with exponents related to the operators' scaling dimensions. In contrast, in the case of a U(1) symmetry group, the corrections only decay logarithmically with system size, with model-dependent prefactors.
  arXiv  Detail & Related papers  (2020-10-20T12:18:26Z)
• Gaussian Process States: A data-driven representation of quantum many-body physics [59.7232780552418]
  We present a novel, non-parametric form for compactly representing entangled many-body quantum states. The state is found to be highly compact, systematically improvable and efficient to sample. It is also proven to be a universal approximator' for quantum states, able to capture any entangled many-body state with increasing data set size.
  arXiv  Detail & Related papers  (2020-02-27T15:54:44Z)

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.