Entanglement entropy in gauge theories and the holographic principle for electric strings
By P. Buividovich, M. Polikarpov. 2008
217 citations recorded by the source corpus.
Abstract We consider quantum entanglement between gauge fields in some region of space A and its complement B . It is argued that the Hilbert space of physical states of gauge theories cannot be decomposed into a direct product H A ⊗ H B of Hilbert spaces of states localized in A and B . The reason is that elementary excitations in gauge theories—electric strings—are associated with closed loops rather than points in space, and there are closed loops which belong both to A and B . Direct product structure and hence the reduction procedure with respect to the fields in B can only be defined if the Hilbert space of physical states is extended by including the states of electric strings which can open on the boundary of A . The positions of string endpoints on this boundary are the additional degrees of freedom which also contribute to the entanglement entropy. We explicitly demonstrate this for the confining and deconfining phases of the three-dimensional Z 2 lattice gauge theory both numerically and using a simple trial ground state wave function. The entanglement entropy appears to be saturated almost completely by the entropy of string endpoints, thus reminding of a “holographic principle” in quantum gravity and AdS/CFT correspondence.
Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/efe6c331844c82f821bcb3fca871b6ca6e4541a6
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In Astronomy and Astrophysics
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Citations in the corpus
- Decomposition of entanglement entropy in lattice gauge theory (2011, background): “Reference [12] also noted the similarity of the Shannon entropy to the log-dimension term that appeared in Ref.”
- Entanglement entropy and nonabelian gauge symmetry (2014, background): “This splitting was introduced for loop quantum gravity (which can be viewed as an SU(2) gauge theory on a dynamical lattice) in [20], and for discrete abelian gauge theories in [21].”
- Local subsystems in gauge theory and gravity (2016, methodology): “Instead we will follow an approach that has been called the extended Hilbert space construction [17–21].”
- Holographic entanglement entropy: an overview (2009, methodology): “Thus, our holographic approach which can be applied to strongly coupled theories will provide a powerful complementary method.”
- Aspects of entanglement entropy for gauge theories (2015, result): “Here we will follow the approach discussed in [1] (GST), see also [9], which is also related to the earlier work, [3, 4].”
- Geometric entropy and edge modes of the electromagnetic field (2015, methodology): “One approach [31, 32] is to embed the physical Hilbert space into a tensor product of local Hilbert spaces.”