When and why do zero-modes cause a divergence in the entanglement entropy?

• URL: http://arxiv.org/abs/2212.07174v1
• Date: Wed, 14 Dec 2022 11:58:20 GMT
• Title: When and why do zero-modes cause a divergence in the entanglement entropy?
• Authors: Vijay Nenmeli and S. Shankaranarayanan (IIT Bombay)
• Abstract summary: We show that zero modes are necessary, but not sufficient for entanglement entropy divergences. We extend our analysis to Bosonic chains, where we demonstrate that zero modes of the entanglement Hamiltonian provide a signature for divergences independent of the entanglement Hamiltonian. We find that the methods detailed for Bosonic chains have Fermionic analogs and follow this up with a numerical study of the entanglement in the Fermionic chain.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We examine the correlations between divergences in ground state entanglement entropy and emergent zero-modes of the underlying Hamiltonian in the context of one-dimensional Bosonic and Fermionic chains. Starting with a pair of coupled Bosonic degrees of freedom, we show that zero modes are necessary, but not sufficient for entanglement entropy divergences. We then list sufficient conditions that identify divergences. Next, we extend our analysis to Bosonic chains, where we demonstrate that zero modes of the entanglement Hamiltonian provide a signature for divergences independent of the entanglement Hamiltonian. We then generalize our results to one-dimensional Fermionic lattices for a chain of staggered Fermions which is a discretized version of the Dirac field. We find that the methods detailed for Bosonic chains have Fermionic analogs and follow this up with a numerical study of the entanglement in the Fermionic chain. Finally, we discuss our results in light of the factorization algebra theorem.

Related papers

• Entanglement in $(1+1)$-dimensional Free Scalar Field Theory: Tiptoeing between Continuum and Discrete [0.0]
  We show how the formalism developed for the discretized theory can be utilized in order to obtain results in the continuous theory. In a specific coordinate system, the modular Hamiltonian assumes the form of a free field Hamiltonian on the Rindler wedge.
  arXiv  Detail & Related papers  (2024-06-16T18:00:42Z)
• Zero-mode entanglement across a conformal defect [0.0]
  We consider a free-fermion chain with a conformal defect that features an extended zero mode. The zero-mode induced degeneracy modifies the density of states in the single-particle entanglement spectrum. We observe parity effects for half-chains with even/odd sites, which do not decay with size.
  arXiv  Detail & Related papers  (2023-03-18T14:32:01Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Spectral form factor in a minimal bosonic model of many-body quantum chaos [1.3793594968500609]
  We study spectral form factor in periodically-kicked bosonic chains. We numerically find a nontrivial systematic system-size dependence of the Thouless time.
  arXiv  Detail & Related papers  (2022-03-10T15:56:24Z)
• Regularized Zero-Range Hamiltonian for a Bose Gas with an Impurity [77.34726150561087]
  We study the Hamiltonian for a system of N identical bosons interacting with an impurity. We introduce a three-body force acting at short distances. The effect of this force is to reduce to zero the strength of the zero-range interaction between two particles.
  arXiv  Detail & Related papers  (2022-02-25T15:34:06Z)
• Symmetry-resolved entanglement in a long-range free-fermion chain [0.0]
  We study the symmetry-resolved entanglement entropy in the ground state of a fermionic chain. We find entanglement, but comparing with the short-range counterpart its breaking occurs at a different order and it does depend on the hopping amplitudes.
  arXiv  Detail & Related papers  (2022-02-11T19:38:38Z)
• Conformal field theory from lattice fermions [77.34726150561087]
  We provide a rigorous lattice approximation of conformal field theories given in terms of lattice fermions in 1+1-dimensions. We show how these results lead to explicit error estimates pertaining to the quantum simulation of conformal field theories.
  arXiv  Detail & Related papers  (2021-07-29T08:54:07Z)
• 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)
• 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)
• Long-distance entanglement of purification and reflected entropy in conformal field theory [58.84597116744021]
  We study entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy. We find an elementary proof that the decay of both, the entanglement of purification and reflected entropy, is enhanced with respect to the mutual information behaviour.
  arXiv  Detail & Related papers  (2021-01-29T19:00:03Z)

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.