Holographic entanglement of purification near a critical point

Abstract

In the presence of finite chemical potential $$\mu $$ μ , we holographically compute the entanglement of purification in a $$2+1$$ 2 + 1 - and $$3+1$$ 3 + 1 -dimensional field theory and also in a $$3+1$$ 3 + 1 -dimensional field theory with a critical point, at which a phase transition takes place. We observe that compared to $$2+1$$ 2 + 1 - and $$3+1$$ 3 + 1 -dimensional field theories, the behavior of entanglement of purification near critical point is different and it is not a monotonic function of $$\frac{\mu }{T}$$ μ T where T is the temperature of the field theory. Therefore, the entanglement of purification distinguishes the critical point in the field theory. We also discuss the dependence of the holographic entanglement of purification on the various parameters of the theories. Moreover, the critical exponent is calculated.

Entanglement wedge cross section in holographic excited states

“…The above proposals pass a variety of consistency checks which provide important pieces of evidence for finding holographic duals of EWCS. See [13][14][15][16][17][18][19][20] for various studies of general properties of EWCS and its holographic counterparts in static geometries. Further, the nonequilibrium evolution of EWCS for various quench protocols has been considered in [21][22][23][24][25][26].…”

Critical behaviour of hydrodynamic series

“…Different aspects of this background have been investigated. Indeed, it was shown that various quantities such as R-charge conductivity [40], complexity [41], mutual information [42] and entanglement of purification [43,44] remain finite, while their slopes diverge at the critical point with the same critical exponent θ = 1 2 . The value of the dynamical critical exponent was also confirmed in [45] and [46] by studying the non-hydrodynamical quasi normal modes (QNMs) of the external fields and quantum quench in this background, respectively.…”

“…As mentioned before, the theory we study in this paper enjoys a critical point at µ = πT / √ 2. The behavior of different observables near this critical point has been studied in [40][41][42][43][44][45][46]. In all cases it was shown that the critical exponent is θ = 1 2 .…”

Long-distance entanglement of purification and reflected entropy in conformal field theory

“…To date, its understanding in the intersection of quantum information science and high-energy physics is based on Gaussian calculations [27][28][29], usage of CFT techniques with a limited range of applicability [30][31][32] and, finally, on a conjectured realization in holography [33,34]. It is worth pointing out that in the latter case, EoP is conjectured to be dual to the entanglement wedge cross section [35][36][37][38] for which a variety of results have been found ranging from connections with multipartite states to thermal states (see e.g., [39][40][41][42][43][44][45][46][47][48][49]) and is thus pivotal to the efforts of understanding bulk reconstruction in holography [50]. The aim of this letter is to to elucidate what perhaps is the simplest setting in which EoP behaves universally across CFTs and does not rely on Gaussianity nor on local conformal transformations.…”