Holographic Mutual Information Research Articles

Holographic two-point functions in medium

In this paper, we study two-point correlation function in a medium composed of two kinds of matter, which is the dual of a three-dimensional generalized p-brane gas geometry. Following the holographic prescription, we calculate temporal and spatial two-point functions in the medium. In general, the screening effect of the medium makes two-point functions decreases more rapidly than the CFTs two-point function. In the extremal limit, however, we find that a temporal two-point function is still conformal. This indicates that a two-dimensional UV CFT flows into a one-dimensional quantum mechanics in the IR limit. This is consistent with the fact that the near horizon geometry in the extremal limit reduces to AdS2. We also investigate holographic mutual information representing the correlation between two subsystems. We show that a critical distance in the IR region, where the mutual information vanishes, leads to a similar behavior to the correlation length of a two-point function.

Mixed state entanglement measures for the dipole deformed supersymmetric Yang–Mills theory

Two different entanglement measures for mixed states, namely, the entanglement of purification and entanglement negativity has been holographically computed for the dipole deformed supersymmetric Yang–Mills (SYM) theory by considering its gravity dual. The dipole deformation induces non-locality in the SYM theory which is characterized by a length-scale a=λ12L̃. Considering a strip like subsystem of length la (in dimensionless form), we first analytically calculate the holographic entanglement entropy for and compare the obtained results with that of obtained numerically. The analytical calculations have been carried out by considering aut≤1, 1≤aut<aub and aut∼aub, where aub is the UV cut-off. The choice of these regions enable us to identify the expansion parameters needed to carry out binomial expansions. The entanglement measures expectedly displays a smooth behaviour with respect to the subsystem size as the geometry has a smooth transition between the mentioned regions. Using these results, the holographic mutual information is then computed for two disjoint subsystems A and B. Based upon the EP=EW duality, the entanglement of purification (EP) is then computed and the effects of dipole deformation in this context have been studied. Finally, we proceed to compute entanglement negativity for this theory and compare the obtained result with that of the standard SYM theory in order to get a better understanding about the effects of the non-locality.

Holographic entanglement entropy for relativistic hydrodynamic flows

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.

A holographic study of the characteristics of chaos and correlation in the presence of backreaction

In this work, we perform a holographic study to estimate the effect of backreaction on the correlation between two subsystems forming the thermofield double (TFD) state. Each of these subsystems is described as a strongly coupled large-Nc thermal field theory, and the backreaction imparted to it is sourced by the presence of a uniform distribution of heavy static quarks. The TFD state we consider here holographically corresponds to an entangled state of two AdS blackholes, each of which is deformed by a uniform distribution of static strings. In order to make a holographic estimation of correlation between two entangled boundary field theories in presence of backreaction we compute the holographic mutual information in the backreacted eternal blackhole. The late time exponential growth of an early perturbation is a signature of chaos in the boundary thermal field theory. Using the shock wave analysis in the dual bulk theory, we characterize this chaotic behaviour by computing the holographic butterfly velocity. We find that there is a reduction in the butterfly velocity due to a correction term that depends on the backreaction parameter. The late time exponential growth of an early perturbation destroys the two-sided correlation, whereas the backreaction always acts in favour of it. Finally we compute the entanglement velocity that essentially encodes the rate of disruption of correlation between two boundary theories.

Probing phase structure of strongly coupled matter with holographic entanglement measures

We study the holographic entanglement measures such as the holographic mutual information, HMI, and the holographic entanglement of purification, EoP, in a holographic QCD model at finite temperature and zero chemical potential. This model can realize various types of phase transitions including crossover, first order and second order phase transitions. We use the HMI and EoP to probe the phase structure of this model and we find that at the critical temperature they can characterize the phase structure of the model. Moreover we obtain the critical exponent using the HMI and EoP.

Quantum correlation in quark–gluon medium

We study the thermodynamics and quantum correlations of the string cloud geometry whose field theory dual is the quark–gluon medium. We found the novel universality of the entanglement entropy first law in the high quark density limit. We also showed that a correlation function generally decreases as the entanglement entropy of the background medium increases due to the screening effect of the background. We study the UV and IR effects of the medium on phase transition behaviour observed in the holographic mutual information using both perturbative and numerical computations. Moreover, by numerical computation, we show that in the IR region the critical length obtained from the mutual information behaves similar to the correlation length of the two-point function.

Non-conformal behavior of holographic entanglement measures

We evaluate the holographic entanglement entropy, HEE, holographic mutual information, HMI, and holographic entanglement of purification, EoP, in a non-conformal model at zero and finite temperature. In order to find the analytical results we consider some specific regimes of the parameter space. We find that the non-conformal effects decrease the redefined HEE and increase the redefined HMI and EoP in the all studied regimes. On the other side, the temperature effects increase (decrease) the redefined HEE (HMI) in the all studied regimes while it has no definite effect on the redefined EoP. Finally, from the information point of view, we find that in the vicinity of the phase transition the zero temperature state is more favorable than the finite temperature one.

Entanglement wedge cross-section for noncommutative Yang-Mills theory

The signature of noncommutativity on various measures of entanglement has been observed by considering the holographic dual of noncommutative super Yang-Mills theory. We have followed a systematic analytical approach in order to compute the holographic entanglement entropy corresponding to a strip like subsystem of length l. The relationship between the subsystem size (in dimensionless form) frac{l}{a} and the turning point (in dimensionless form) introduces a critical length scale frac{l_c}{a} which leads to three domains in the theory, namely, the deep UV domain (l < lc; aut » 1, aut ∼ aub), deep noncommutative domain (l > lc, aub> aut » 1) and deep IR domain (l > lc, aut « 1). This in turn means that the length scale lc distinctly points out the UV/IR mixing property of the non-local theory under consideration. We have carried out the holographic study of entanglement entropy for each of these domains by employing both analytical and numerical techniques. The broken Lorentz symmetry induced by noncommutativity has motivated us to redefine the entropic c-function. We have obtained the noncommutative correction to the c-function upto leading order in the noncommutative parameter. We have also looked at the behaviour of this quantity over all the domains of the theory. We then move on to compute the minimal cross-section area of the entanglement wedge by considering two dis- joint subsystems A and B. On the basis of EP = EW duality, this leads to the holographic computation of the entanglement of purification. The correlation between two subsystems, namely, the holographic mutual information I(A : B) has also been computed. Moreover, the computations of EW and I(A : B) has been done for each of the domains in the theory. We have then briefly discussed the effect of the UV cut-off on the IR behaviours of these quantities. Finally, we consider a black hole geometry with a noncommutative parameter and study the influence of both noncommutativity and finite temperature on the various measures of quantum entanglement.

Mixed state entanglement and thermal phase transitions

We study the relationship between mixed state entanglement and thermal phase transitions. As a typical example, we compute the holographic entanglement entropy (HEE), holographic mutual information (MI), and the holographic entanglement wedge minimum cross section (EWCS) over the superconductivity phase transition. We find that HEE, MI, and EWCS can all diagnose the superconducting phase transition. They are continuous at the critical point, but their first derivative with respect to temperature is discontinuous. MI decreases with increasing temperature and exhibits a convex behavior, while HEE increases with increasing temperature and exhibits a concave behavior. However, EWCS can exhibit either the same or the opposite behavior as MI, depending on the size of the specific configuration. These results show that EWCS captures more abundant information than HEE and MI. We also provide a new algorithm to compute the EWCS for general configurations.

Entanglement wedge cross section in holographic excited states

We evaluate the entanglement wedge cross section (EWCS) in asymptotically AdS geometries which are dual to boundary excited states. We carry out a perturbative analysis for calculating EWCS between the vacuum and other states for a symmetric configuration consisting of two disjoint strips and obtain analytical results in the specific regimes of the parameter space. In particular, when the states described by purely gravitational excitations in the bulk we find that the leading correction to EWCS is negative and hence the correlation between the boundary subregions decreases. We also study other types of excitations upon adding the extra matter fields including current and scalar condensate. Our study reveals some generic properties of boundary information measures dual to EWCS, e.g., entanglement of purification, logarithmic negativity and reflected entropy. Finally, we discuss how these results are consistent with the behavior of other correlation measures including the holographic mutual information.

Holographic informational properties for a specific Einstein-Maxwell-dilaton gravity theory

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.

Entanglement measures for nonconformal D-branes

We study various entanglement measures associated with certain non-conformal field theories. We consider non-conformal D$p$-brane backgrounds, which are dual to these field theories, for our holographic analysis. Restricting our interests in $p=1,2,4$, we explicitly compute properties of holographic entanglement entropy and entanglement wedge cross section, $\text{E}_{W}$, corresponding to two parallel strip shaped boundary subregions in these set ups. We study low and high temperature behaviours of these quantities analytically as well as using numerical methods. In all cases, the $\text{E}_{W}$ decrease monotonically with temperature. We observe discontinuous jumps in $\text{E}_{W}$ while the width of (as well as the separation between) the subregions reach critical values in all the cases considered. However, the corresponding holographic mutual information $\texttt{I}_{M}$ continuously decreases to zero for the aforementioned configurations. We also notice that the conjectured inequality $\text{E}_{W} \geq \texttt{I}_{M}/2$ still holds for non-conformal field theories as well. We analytically determine the critical separation between these subregions that triggers a phase transition in the holographic mutual information.

Holographic mutual information and critical exponents of the strongly coupled plasma

This note contains discussions on the entanglement entropy and mutual information of a strongly coupled field theory with a critical point which has a holographic dual. We investigate analytically, in the specific regimes of parameters, how these non-local operators behave near the critical point. Interestingly, we observe that although the mutual information is constant at the critical point, its slope shows a power-law divergence in the vicinity of the critical point. We show that the leading behavior of mutual information at and near the critical point could yield a set of critical exponents if we regard it as an order parameter. Our result for this set of static critical exponents is (1/2,1/2,1/2,2) which is identical to the one calculated via the thermodynamic quantities. Hence it suggests that beside the numerous merits of mutual information, this quantity also captures the critical behavior of the underlying field theory and it could be used as a proper measure to probe the phase structure associated with the strongly coupled systems.

On Casimir Energy and Mutual Information in Non-relativistic Backgrounds

We apply the AdS/CFT correspondence in considering the Casimir energy and some non-local entanglement measures in the non-relativistic backgrounds for general dynamical exponent z with and without hyperscaling violation exponent 𝜃. In such background, we use holographic methods and compute the mutual information and tripartite information. We also consider the monogamy of holographic mutual information in the Schrodinger-type geometry and by numerical analysis we show that this quantity is monogamous.

Large-d phase transitions in holographic mutual information

In the AdS/CFT correspondence, the entanglement entropy of subregions in the boundary CFT is conjectured to be dual to the area of a bulk extremal surface at leading order in GN in the holographic limit. Under this dictionary, distantly separated regions in the CFT vacuum state have zero mutual information at leading order, and only attain nonzero mutual information at this order when they lie close enough to develop significant classical and quantum correlations. Previously, the separation at which this phase transition occurs for equal-size ball-shaped regions centered at antipodal points on the boundary was known analytically only in 3 spacetime dimensions. Inspired by recent explorations of general relativity at large-d, we compute the separation at which the phase transition occurs analytically in the limit of infinitely many spacetime dimensions, and find that distant regions cannot develop large correlations without collectively occupying the entire volume of the boundary theory. We interpret this result as illustrating the spatial decoupling of holographic correlations in the large-d limit, and provide intuition for this phenomenon using results from quantum information theory. We also compute the phase transition separation numerically for a range of bulk spacetime dimensions from 4 to 21, where analytic results are intractable but numerical results provide insight into the dimension-dependence of holographic correlations. For bulk dimensions above 5, our exact numerical results are well approximated analytically by working to next-to-leading order in the large-d expansion.

Higher-curvature corrections to holographic mutual information

In this paper, we study some non-local measurements of quantum correlations in extended gravities with higher-order curvature terms, including conformal gravity. Precisely, we consider higher-curvature correction on holographic mutual information in conformal gravity. There is in fact one deformation in the states because of the higher-curvature corrections. Here by making use of the holographic methods, we study the deformation in the holographic mutual information due to the higher-curvature terms. We also address the change in the quantum phase transition due to these deformations.

Effect of massive potentials and the Gauss–Bonnet gravity on the holographic thermalization

We perform a numerical study to recognize the difference between various massive potentials in the massive gravity on the holographic thermalization in the AdS and AdS–Gauss–Bonnet gravities in 4[Formula: see text]+[Formula: see text]1 dimensions. In this space–time, three different massive potentials contribute to the graviton mass. We analyze the effects of these terms on the time evolution of entanglement entropy and the corresponding thermalization time. We also trace the effect of Gauss–Bonnet coupling on the thermalization process. The behavior of the holographic mutual information and size of the kinks, appearing in a large interval, are also studied.

The effect of anisotropy on holographic entanglement entropy and mutual information

We study the effect of anisotropy on holographic entanglement entropy (HEE) and holographic mutual information (MI) in the Q-lattice model, by exploring the HEE and MI for infinite strips along arbitrary directions. We find that the lattice always enhances the HEE. The MI, however, is enhanced by lattice for large sub-regions; while for small sub-regions, the MI is suppressed by the lattice. We also discuss how these phenomena result from the deformation of geometry caused by Q-lattices.

Holographic entanglement negativity conjecture for adjacent intervals in AdS3/CFT2

We propose a holographic entanglement negativity conjecture involving the bulk geometry, for mixed states of adjacent intervals in (1+1)-dimensional dual conformal field theories through the AdS/CFT correspondence. The holographic entanglement negativity is obtained from a specific algebraic sum of the geodesics anchored on respective intervals on the boundary which reduces to the holographic mutual information between them. Utilizing our conjecture we obtain the entanglement negativity of adjacent intervals in zero and finite temperature (1+1)-dimensional holographic conformal field theories dual to the bulk AdS3 vacuum and the Euclidean BTZ black hole respectively. Our holographic conjecture exactly reproduces the conformal field theory results obtained through the replica technique, in the large central charge limit. We briefly elucidate the corresponding issue for the AdSd+1/CFTd scenario.

Holographic approach to entanglement entropy in disordered systems

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 leads to a sub-leading 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 sub-leading 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.