Entanglement in Lifshitz-type quantum field theories

Mozaffar, M. Reza Mohammadi; Mollabashi, Ali

doi:10.1007/jhep07(2017)120

Cited by 70 publications

(73 citation statements)

References 59 publications

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“…Such a behavior is not surprising because as discussed in [45] the spatial correlations between subregions become stronger for larger values of z. On the other hand as is clear from the graphs, E W is monotonically decreasing as the hyperscaling violating exponent increases.…”

Section: Low and High Temperature Behavior Of Ewcsmentioning

confidence: 60%

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Some aspects of entanglement wedge cross-section

Velni

Mozaffar

Vahidinia

2019

J. High Energ. Phys.

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We consider the minimal area of the entanglement wedge cross section (EWCS) in Einstein gravity. In the context of holography, it is proposed that this quantity is dual to different information measures, e.g., entanglement of purification, logarithmic negativity and reflected entropy. Motivated by these proposals, we examine in detail the low and high temperature corrections to this quantity and show that it obeys the area law even in the finite temperature. We also study EWCS in nonrelativistic field theories with nontrivial Lifshitz and hyperscaling violating exponents. The resultant EWCS is an increasing function of the dynamical exponent due to the enhancement of spatial correlations between subregions for larger values of z. We find that EWCS is monotonically decreasing as the hyperscaling violating exponent increases. We also obtain this quantity for an entangling region with singular boundary in a three dimensional field theory and find a universal contribution where the coefficient depends on the central charge. Finally, we verify that for higher dimensional singular regions the corresponding EWCS obeys the area law.where G N is the Newton constant and Γ A is a codimension-2, spacelike minimal hypersurface in the bulk spacetime, anchored to the asymptotic boundary such that ∂Γ A = ∂A (see figure 1). The RT proposal which passes a variety of consistency tests, generalizes to time dependent case [2] and higher derivative theories of gravity [3][4][5][6]. Using these prescriptions, the correlation of several disconnected components can also be considered. In particular when the entangling region is made by two disjoint spatial components, an important quantity to study is the holographic mutual

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Section: Low and High Temperature Behavior Of Ewcsmentioning

confidence: 60%

“…It is worth to mention that various aspects of entanglement measures in QFTs with Lifshitz scaling symmetry are studied in[45][46][47][48].…”

mentioning

confidence: 99%

Some aspects of entanglement wedge cross-section

Velni

Mozaffar

Vahidinia

2019

J. High Energ. Phys.

Self Cite

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“…This happens as the critical exponent assumes z ± = (3 ± √ 13)/2, or approximately, z − ≃ −0.3 or z + ≃ 3.3. Non integer critical exponents have appeared in previous studies, e.g., [33,[48][49][50][51] -and references therein. Specially in [48,49] the authors argue that although the Lifshitz critical exponents in the action of a quantum field theory developing Lifshitz symmetry are assumed to be integer, there is no such limitation indeed since the obtained dispersion relation in the Hamiltonian density associated with the quantized theory shows the exact analytic continuation to non integer values of z.…”

Section: Viscosity/entropy Density Ratiomentioning

confidence: 93%

Black brane in asymptotically Lifshitz spacetime and viscosity/entropy ratios in Horndeski gravity

Brito¹,

Santos²

2020

EPL

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We investigate black brane solutions in asymptotically Lifshitz spacetime in 3+1dimensional Horndeski gravity, which parameters are related to the cosmological constant as α = γΛ and depend on arbitrary values of the dynamical critical exponent z since Λ = −(1 + 2z)/L 2 . For the case z = 1 we recover black brane solutions in asymptotically AdS 4 spacetime. We also investigate the shear viscosity in the 2+1dimensional dual boundary field theory via holographic correspondence. We show that for arbitrary values of AdS radius L, only two specific critical exponents are allowed: z = −0.3 or z = 3.3. At the former value, we find that the bound for viscosity to entropy density ratio η/s ≥ 1/(4π) is violated.

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“…In this subsection, we introduce a Hamiltonian of Lifshitz free scalar theories on 1 dimensional lattice based on [35,36,39]. Let us first start with a Hamiltonian of Lifshitz free scalar field theories in 1 spacial dimension 4…”

Section: Hamiltonian and Equation Of Lifshitz Free Scalar Theoriesmentioning

confidence: 99%

Entanglement after quantum quenches in Lifshitz scalar theories

Kim¹,

Nishida²,

Seo³

et al. 2019

J. Stat. Mech.

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We study the time evolution of the entanglement entropy after quantum quenches in Lifshitz free scalar theories, with the dynamical exponent z > 1, by using the correlator method. For quantum quenches we consider two types of time-dependent mass functions: end-critical-protocol (ECP) and cis-critical-protocol (CCP). In both cases, at early times the entanglement entropy is independent of the subsystem size. After a critical time (t c ), the entanglement entropy starts depending on the subsystem size significantly. This critical time t c for z = 1 in the fast ECP and CCP has been explained well by the fast quasi-particle of the quasi-particle picture. However, we find that for z > 1 this explanation does not work and t c is delayed. We explain why t c is delayed for z > 1 based on the quasiparticle picture: in essence, it is due to the competition between the fast and slow quasiparticles. At late times, in the ECP, the entanglement entropy slowly increases while, in the CCP, it is oscillating with a well defined period by the final mass scale, independently of z. We give an interpretation of this phenomena by the correlator method. As z increases, the entanglement entropy increases, which can be understood by long-range interactions due to z. arXiv:1906.05476v2 [hep-th]

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Entanglement in Lifshitz-type quantum field theories

Cited by 70 publications

References 59 publications

Some aspects of entanglement wedge cross-section

Some aspects of entanglement wedge cross-section

Black brane in asymptotically Lifshitz spacetime and viscosity/entropy ratios in Horndeski gravity

Entanglement after quantum quenches in Lifshitz scalar theories

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