Entanglement and confinement in lattice gauge theory tensor networks
- URL: http://arxiv.org/abs/2401.01930v2
- Date: Fri, 23 Feb 2024 19:15:28 GMT
- Title: Entanglement and confinement in lattice gauge theory tensor networks
- Authors: Johannes Knaute, Matan Feuerstein and Erez Zohar
- Abstract summary: We show how the long-range behavior of quantities gives rise to an entanglement area law in both the thermodynamic limit and in the continuum.
We numerically demonstrate the applicability of our method to the $Z$ lattice gauge theory and relate some entanglement properties to the confinement-deconfinement transition therein.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We develop a transfer operator approach for the calculation of R\'enyi
entanglement entropies in arbitrary (i.e. Abelian and non-Abelian) pure lattice
gauge theory projected entangled pair states in 2+1 dimensions. It is
explicitly shown how the long-range behavior of these quantities gives rise to
an entanglement area law in both the thermodynamic limit and in the continuum.
We numerically demonstrate the applicability of our method to the $Z_2$ lattice
gauge theory and relate some entanglement properties to the
confinement-deconfinement transition therein. We provide evidence that R\'enyi
entanglement entropies in certain cases do not provide a complete probe of
(de)confinement properties compared to Wilson loop expectation values as other
genuine (nonlocal) observables.
Related papers
- Duality transformations and the entanglement entropy of gauge theories [0.0]
We study lattice gauge theories that admit a dual description in terms of spin models.
In the first part, we perform the duality transformation in a replica geometry, deriving the structure of a replica space for a gauge theory.
In the second part, we calculate by means of Monte Carlo simulations, the entropic c-function of the $Z$ gauge theory in three spacetime dimensions.
arXiv Detail & Related papers (2024-04-02T14:24:51Z) - Confinement in the Transverse Field Ising model on the Heavy Hex lattice [0.0]
We study the emergence of confinement in the transverse field Ising model on a decorated hexagonal lattice.
We show how a quench from a broken symmetry state leads to striking nonthermal behaviour underpinned by persistent oscillations and saturation of the entanglement entropy.
arXiv Detail & Related papers (2024-02-02T16:50:20Z) - Canonical Momenta in Digitized SU(2) Lattice Gauge Theory: Definition
and Free Theory [0.0]
Hamiltonian simulations of quantum systems require a finite-dimensional representation of the operators acting on the Hilbert space H.
Here we give a prescription for gauge links and canonical momenta of an SU(2) gauge theory.
We show that the fundamental commutation relations are fulfilled up to discretisation artefacts.
arXiv Detail & Related papers (2023-04-05T09:25:20Z) - Non-Abelian symmetry can increase entanglement entropy [62.997667081978825]
We quantify the effects of charges' noncommutation on Page curves.
We show analytically and numerically that the noncommuting-charge case has more entanglement.
arXiv Detail & Related papers (2022-09-28T18:00:00Z) - Annihilating Entanglement Between Cones [77.34726150561087]
We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied.
Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
arXiv Detail & Related papers (2021-10-22T15:02:39Z) - 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) - Entanglement Entropy of Non-Hermitian Free Fermions [59.54862183456067]
We study the entanglement properties of non-Hermitian free fermionic models with translation symmetry.
Our results show that the entanglement entropy has a logarithmic correction to the area law in both one-dimensional and two-dimensional systems.
arXiv Detail & Related papers (2021-05-20T14:46:09Z) - 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) - Real-time dynamics in 2+1d compact QED using complex periodic Gaussian
states [0.688204255655161]
We introduce a class of variational states to study ground state properties and real-time dynamics in (2+1)-dimensional compact QED.
We calculate the ground state energy density for lattice sizes up to $20 times 20$ and extrapolate to the thermodynamic limit for the whole coupling region.
arXiv Detail & Related papers (2020-06-17T17:58:08Z) - Generalized Entanglement, Charges and Intertwiners [0.0]
We define a measure of entanglement entropy as a measure of information erased under restriction to a subspace of observables.
We argue that the correct entanglement measure in the presence of charges is the sum of two terms; one measuring the entanglement of charge-neutral operators, and the other measuring the contribution of the bi-local intertwiners.
arXiv Detail & Related papers (2020-05-22T20:49:05Z)
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.