Volume law for the entanglement entropy in non-local QFTs

In this paper we study the conjectural relation between confinement in a quantum field theory and the presence of a phase transition in its corresponding entanglement entropy. We determine the sufficient conditions for the latter and compare to the conditions for having a confining Wilson line. We demonstrate the relation in several examples. Superficially, it may seem that certain confining field theories with a non-local high energy behavior, like the dual of D5 branes wrapping a two-cycle, do not admit the corresponding phase transition. However, upon closer inspection we find that, through the introduction of a regulating UV-cutoff, new eight-surface configurations appear, that satisfy the correct concavity condition and recover the phase transition in the entanglement entropy. We show that a local-UV-completion to the confining non-local theories has a similar effect to that of the aforementioned cutoff.

Section: Jhep06(2014)005supporting

confidence: 61%

Confinement, phase transitions and non-locality in the entanglement entropy

Kol

Núñez

Schofield

et al. 2014

“…7 The model of our interest for large dynamical JHEP07(2017)120 exponents is similar to a certain non-local scalar theory studied in [40]. In figure 4 we have shown that this scaling behavior also happens for Renyi entropies for large values of z.…”

Section: Review Of Correlator Methodsmentioning

confidence: 58%

“…Volume law scaling of entanglement entropy has been previously observed in several field theories with nonlocal effects [40][41][42][43][44] (See also [45] for a perturbative study of entanglement entropy in nonlocal theories.). 7 The model of our interest for large dynamical JHEP07(2017)120 exponents is similar to a certain non-local scalar theory studied in [40].…”

Section: Review Of Correlator Methodsmentioning

confidence: 84%

Entanglement in Lifshitz-type quantum field theories

Mozaffar

Mollabashi

2017

Abstract:We study different aspects of quantum entanglement and its measures, including entanglement entropy in the vacuum state of a certain Lifshitz free scalar theory. We present simple intuitive arguments based on "non-local" effects of this theory that the scaling of entanglement entropy depends on the dynamical exponent as a characteristic parameter of the theory. The scaling is such that in the massless theory for small entangling regions it leads to area law in the Lorentzian limit and volume law in the z → ∞ limit. We present strong numerical evidences in (1+1) and (2+1)-dimensions in support of this behavior. In (2 + 1)-dimensions we also study some shape dependent aspects of entanglement. We argue that in the massless limit corner contributions are no more additive for large enough dynamical exponent due to non-local effects of Lifshitz theories. We also comment on possible holographic duals of such theories based on the sign of tripartite information.

“…In string theory examples of AdS/CFT, a gravity dual usually includes an internal compact space in addition to the AdS spacetime, as is typical in the AdS 5 × S 5 type IIB string background dual to the four dimensional N = 4 super Yang-Mills. Therefore one may wonder how quantum entanglement in CFTs can probe internal spaces such as S 5 . As we will discuss in the final part of this paper, this question is closely related to the entanglement entropy between two interacting CFTs (1.3).…”

Section: Jhep04(2014)185mentioning

confidence: 99%

“…For example, this quantity follows the area law [1][2][3][4] if we consider a local quantum field theory with a UV fixed point, while non-local field theories [5,6] or QFTs with fermi surfaces [7,8] at UV cut off scale can violate the area law. Moreover, the coefficients of logarithmically divergent terms of S A in even dimensional conformal field theories (CFTs) are proportional to central charges [9][10][11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Entanglement between two interacting CFTs and generalized holographic entanglement entropy

Mollabashi

Shiba

Takayanagi

2014

Self Cite

109

In this paper we discuss behaviors of entanglement entropy between two interacting CFTs and its holographic interpretation using the AdS/CFT correspondence. We explicitly perform analytical calculations of entanglement entropy between two free scalar field theories which are interacting with each other in both static and time-dependent ways. We also conjecture a holographic calculation of entanglement entropy between two interacting N = 4 super Yang-Mills theories by introducing a minimal surface in the S 5 direction, instead of the AdS 5 direction. This offers a possible generalization of holographic entanglement entropy.