Entanglement Entropy for 2D Gauge Theories with Matters

@article{Aoki2017EntanglementEF,
  title={Entanglement Entropy for 2D Gauge Theories with Matters},
  author={Sinya Aoki and Norihiro Iizuka and Kotaro Tamaoka and Tsuyoshi Yokoya},
  journal={Physical Review D},
  year={2017},
  volume={96},
  pages={045020}
}
We investigate the entanglement entropy in 1+1-dimensional $SU(N)$ gauge theories with various matter fields using the lattice regularization. Here we use extended Hilbert space definition for entanglement entropy, which contains three contributions; (1) classical Shannon entropy associated with superselection sector distribution, where sectors are labelled by irreducible representations of boundary penetrating fluxes, (2) logarithm of the dimensions of their representations, which is… 

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References

SHOWING 1-10 OF 24 REFERENCES

Aspects of entanglement entropy for gauge theories

A bstractA definition for the entanglement entropy in a gauge theory was given recently in arXiv:1501.02593. Working on a spatial lattice, it involves embedding the physical state in an extended

Entanglement entropy in (3 + 1)-d free U(1) gauge theory

A bstractWe consider the entanglement entropy for a free U(1) theory in 3+1 dimensions in the extended Hilbert space definition. By taking the continuum limit carefully we obtain a replica trick path

Decomposition of entanglement entropy in lattice gauge theory

We consider entanglement entropy between regions of space in lattice gauge theory. The Hilbert space corresponding to a region of space includes edge states that transform nontrivially under gauge

Entanglement entropy for pure gauge theories in 1+1 dimensions using the lattice regularization

We study the entanglement entropy (EE) for pure gauge theories in 1+1 dimensions with the lattice regularization. Using the definition of the EE for lattice gauge theories proposed in a previous

On the definition of entanglement entropy in lattice gauge theories

A bstractWe focus on the issue of proper definition of entanglement entropy in lattice gauge theories, and examine a naive definition where gauge invariant states are viewed as elements of an

Entanglement in weakly coupled lattice gauge theories

A bstractWe present a direct lattice gauge theory computation that, without using dualities, demonstrates that the entanglement entropy of Yang-Mills theories with arbitrary gauge group G contains a

On the entanglement entropy for gauge theories

A bstractWe propose a definition for the entanglement entropy of a gauge theory on a spatial lattice. Our definition applies to any subset of links in the lattice, and is valid for both Abelian and

Entanglement entropy of a Maxwell field on the sphere

We compute the logarithmic coefficient of the entanglement entropyon a sphere for a Maxwell field in d = 4 dimensions. In spherical coordinates the problem decomposes into one dimensional ones along

Holographic derivation of entanglement entropy from the anti-de Sitter space/conformal field theory correspondence.

It is argued that the entanglement entropy in d + 1 dimensional conformal field theories can be obtained from the area of d dimensional minimal surfaces in AdS(d+2), analogous to the Bekenstein-Hawking formula for black hole entropy.