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arXiv:2211.14271 · Journal of High Energy Physics

Holographic entanglement entropy for relativistic hydrodynamic flows

Jyotirmoy Bhattacharya, Parthajit Biswas, A. Chandranathan, Sayan Das

Published May 11, 2023• 1 citation
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Abstract

Abstract We study the behaviour of holographic entanglement entropy (HEE) in near equilibrium thermal states which are macroscopically described by conformal relativistic hydrodynamic flows dual to dynamical black brane geometries. We compute HEE for strip-shaped subsystems in boundary dimensions d = 2, 3, 4, which provides us with general qualitative inferences on the interplay between fluid flows and entanglement dynamics. At first, we consider the zeroth order in hydrodynamic derivative expansion, holographically described by stationary boosted black branes. Working non-perturbatively in fluid velocity, we find that, as the fluid velocity approaches its relativistic upper limit, the UV regulated HEE exhibits a divergence at arbitrary temperature. Also, the holographic mutual information between two relatively close subsystems vanishes at some critical fluid velocity and remains zero beyond it. We then compute HEE in an excited state of the fluid in the presence of the sound mode. As a simplified setup, we first work with non-dissipative dynamics in d = 2, where the time evolution of HEE is studied in the presence of the sound mode and a propagating pressure pulse. In d = 4, working upto first order in derivative expansion, we find that dissipative sound modes produce an additional dynamical UV divergence which is subleading compared to the ‘area law divergence’. No such divergence is observed for dissipative sound mode in d = 3.

DOI
10.1007/jhep05(2023)092

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Abstract We study the behaviour of holographic entanglement entropy (HEE) in near equilibrium thermal states which are macroscopically described by conformal relativistic hydrodynamic flows dual to dynamical black brane geometries. We compute HEE for strip-shaped subsystems in boundary dimensions d = 2, 3, 4, which provides us with general qualitative inferences on the interplay between fluid flows and entanglement dynamics. At first, we consider the zeroth order in hydrodynamic derivative expansion, holographically described by stationary boosted black branes. Working non-perturbatively in fluid velocity, we find that, as the fluid velocity approaches its relativistic upper limit, the UV regulated HEE exhibits a divergence at arbitrary temperature. Also, the holographic mutual information between two relatively close subsystems vanishes at some critical fluid velocity and remains zero beyond it. We then compute HEE in an excited state of the fluid in the presence of the sound mode. As a simplified setup, we first work with non-dissipative dynamics in d = 2, where the time evolution of HEE is studied in the presence of the sound mode and a propagating pressure pulse. In d = 4, working upto first order in derivative expansion, we find that dissipative sound modes produce an additional dynamical UV divergence which is subleading compared to the ‘area law divergence’. No such divergence is observed for dissipative sound mode in d = 3.
We study the holographic entanglement entropy and mutual information for Lorentz boosted subsystems. In holographic CFTs at zero and finite temperature, we find that the mutual information gets divergent in a universal way when the end points of two subsystems are light-like separated. In Lifshitz and hyperscaling violating geometries dual to non-relativistic theories, we show that the holographic entanglement entropy is not well-defined for Lorentz boosted subsystems in general. This strongly suggests that in non-relativistic theories, we cannot make a real space factorization of the Hilbert space on a generic time slice except the constant time slice, as opposed to relativistic field theories.
A bstract We consider holographic entanglement entropy in AdS black hole backgrounds by using the limit of large number of dimensions. By dividing the geometry to two patches (with one patch covering the vicinity of the black hole horizon and another covering the other regions), we are able to obtain fully analytic expressions for the entropy when the entanglement region is a strip. We argue that apart from conformal field theories at finite temperature in high number of dimensions, our method works for nearly critical theories in 3+1 dimensions. In the case of extremal black holes, dual to quantum critical systems, the results take a particularly simple form. We also comment on the case of soliton geometries. Finally, we analyze entanglement entropy for wide strips, and propose a general formula for the first subleading term in the expansion of the entropy in (inverse) system size for generic entanglement regions.
We use holographic duality to study the entanglement entropy (EE) of Conformal Field Theories (CFTs) in various spacetime dimensions d, in the presence of various deformations: a relevant Lorentz scalar operator with constant source, a temperature T , a chemical potential μ, a marginal Lorentz scalar operator with source linear in a spatial coordinate, and a circle-compactified spatial direction. We consider EE between a strip or sphere sub-region and the rest of the system, and define the “entanglement density” (ED) as the change in EE due to the deformation, divided by the sub-region’s volume. Using the deformed CFTs above, we show how the ED’s dependence on the strip width or sphere radius, L, is useful for characterizing states of matter. For example, the ED’s small-L behavior is determined either by the dimension of the perturbing operator or by the first law of EE. For Lorentz-invariant renormalization group (RG) flows between CFTs, the “area theorem” states that the coefficient of the EE’s area law term must be larger in the UV than in the IR. In these cases the ED must therefore approach zero from below as L→∞. However, when Lorentz symmetry is broken and the IR fixed point has different scaling from the UV, we find that the ED often approaches the thermal entropy density from above, indicating area theorem violation.
We investigate the entanglement entropy of a two-dimensional disordered system holographically. In particular, we study the evolution of the entanglement entropy along renormalization group flows for a conformal theory at the UV fixed point, that is perturbed by weak disorder into a Lifshitz theory at the IR fixed point. Through numerical fitting, we find that the disorder correlations lead to a subleading power-law term in the entanglement entropy that vanishes at the IR fixed point. Interestingly, the exponent that controls the power-law vanishing of the subleading term seems to be almost universal as it depends very weakly on the strength of the disorder. We show that our results can be put in the context of the c-theorem by defining an effective central charge that decreases along the RG flow. We also investigate disorder induced long-range correlations between the two subsystems by studying the holographic mutual information.
We study the holographic information quantities, including the holographic entanglement entropy (HEE), the holographic mutual information (HMI) and the minimum cross section of the entanglement wedge (EWCS), over a special black brane geometry, which has a vanishing ground-state entropy. Thanks to the zero entropy density at the ground state, we expect to extract novel, even singular informational properties in the zero-temperature limit. Surprisingly, we do not observe any singular behavior of entanglement-related physical quantities in the zero-temperature limit. Nevertheless, we find a peculiar property from this model that in the low-temperature region, the HEE decreases with the temperature, which is contrary to that in most holographic models. We argue that this novel phenomenon is brought by the singular property of the zero-temperature limit. In addition, we also compare the features of the information quantities in this special black brane geometry with those in Reissner-Nordstrom anti--de Sitter (RN-AdS) black brane geometry. It is shown that the HEE and HMI of this vanishing ground-state entropy model are always larger than those of RN-AdS geometry, while the EWCS behaves oppositely. Our results indicate that the HMI and EWCS could have different abilities in describing mixed state entanglement.
We study various entanglement measures associated with certain nonconformal field theories. We consider nonconformal Dp\mathrm{D}pDp-brane backgrounds, which are dual to these field theories, for our holographic analysis. Restricting our interests in p=1p=1p=1, 2, 4, we explicitly compute properties of holographic entanglement entropy and the entanglement wedge cross section, EW{\mathrm{E}}_{W}EW​, corresponding to two parallel strip shaped boundary subregions in these setups. We study low and high temperature behaviors of these quantities analytically as well as by using numerical methods. In all cases, the EW{\mathrm{E}}_{W}EW​ decreases monotonically with temperature. We observe discontinuous jumps in EW{\mathrm{E}}_{W}EW​, while the width of (as well as the separation between) the subregions reaches critical values in all the cases considered. However, the corresponding holographic mutual information IM{\mathtt{I}}_{M}IM​ continuously decreases to zero for the aforementioned configurations. We also notice that the conjectured inequality ${\mathrm{E}}_{W}\ensuremath{\ge}{\mathtt{I}}_{M}/2$ still holds for nonconformal field theories as well. We analytically determine the critical separation between these subregions that triggers a phase transition in the holographic mutual information.