Holographic Entanglement Research Articles

Holographic confining-deconfining gauge theories and entanglement measures with a magnetic field

Holographic confining-deconfining gauge theories and entanglement measures with a magnetic field

The mixed-state entanglement in holographic p-wave superconductor model

In this paper, we investigate the mixed-state entanglement in a model of p-wave superconductivity phase transition using holographic methods. We calculate several entanglement measures, including holographic entanglement entropy (HEE), mutual information (MI), and entanglement wedge cross-section (EWCS). Our results show that these measures display critical behavior at the phase transition points, with the EWCS exhibiting opposite temperature behavior compared to the HEE. Furthermore, we explore the behavior of thermodynamics and holographic quantum information at the zeroth-order phase transition point and find that it is opposite to that observed in the first-order phase transition. Additionally, we find that the critical exponents of all entanglement measures are twice those of the condensate. Our findings also suggest that the EWCS is a more sensitive indicator of the critical behavior of phase transitions than the HEE. Lastly, we uncover a universal inequality in the growth rates of EWCS and MI near critical points in thermal phase transitions, such as p-wave and s-wave superconductivity, suggesting that MI captures more information than EWCS when a phase transition first occurs.

Holographic entanglement entropy and mutual information in deformed field theories at finite temperature

In this paper we have studied the effect of deformation and temperature on holographic entanglement entropy and mutual information between two subsystems in a deformed field theory at finite temperature. The $T\overline{T}$ deformation operator in field theory introduces a cutoff in the dual gravity background. We define different regimes of parameters and calculate the entanglement entropy and mutual information analytically. We observe that temperature and deformation parameter have similar effects on entanglement entropy and mutual information. They both lead to decrease in mutual information or somehow the correlation between the two subsystems. Interestingly we observe the emergence of correction terms in entanglement entropy and mutual information that are universal and do not depend on the scale of the nonlocal operator.

Holographic entanglement entropy in [formula omitted]-deformed AdS3

In this work, we study the holographic entanglement entropy in AdS3 gravity with the certain mixed boundary condition, which turns out to correspond to TT¯-deformed 2D CFTs. By employing the Chern-Simons formalism and Wilson line technique, the holographic entanglement entropy in TT¯-deformed BTZ black hole is obtained. We also get the same formula by calculating the RT surface. The holographic entanglement entropy agrees with the perturbation result derived from both TT¯-deformed CFTs and cutoff AdS3. Moreover, our result shows that the deformed entanglement entropy for large deformation parameter behaves like the entanglement entropy of CFT at zero temperature. We also consider the entanglement entropy of two intervals and study the effect of TT¯ deformation on phase transition.

Aspects of holography in conical AdS3

We study the Feynman propagator of free scalar fields in AdS3 with a conical defect. In the bulk, the defect is represented by a massive particle; in the dual CFT, it is a heavy operator that creates a highly excited state. We construct the propagator by solving the bulk equation of motion in the defect geometry, summing over the modes of the field, and passing to the boundary. The result agrees with a calculation based on the method of images in AdS3/ℤN, where it is also a sum over geodesic lengths. On the boundary, the propagator becomes a semiclassical heavy-light four-point function. We interpret the field modes as double-twist primary states formed by excitations of the scalar on top of the defect, and we check that the correlator is crossing-symmetric by matching its singular behavior to that of the semiclassical Virasoro vacuum block. We also argue that long-range correlations in conical AdS are “thermally” suppressed as the defect becomes more massive by studying the critical behavior of a continuous phase transition in the correlator at the BTZ threshold. Finally, we apply our results to holographic entanglement entropy by exploiting an analogy between free scalars and replica twist fields.

Holographic entanglement entropy and complexity for D-wave superconductors

Using the RT formula and the subregion CV conjecture, we numerically investigate the holographic entanglement entropy (HEE) and holographic subregion complexity (HSC) for two holographic d-wave superconducting models with backreactions. We find that the HEE and HSC can probe these two d-wave superconducting phase transitions. The HEE of the superconducting phase is always lower than that of the normal phase. For the HSC, however, it behaves differently and interestingly, which depends on both the strip-width L_{x} and backreaction kappa . More specifically, when the backreaction is larger than a particular critical value, or the strip-width of the boundary subsystem is smaller than a particular critical value, the HSC in the superconducting phase is larger than that in the normal phase, and vice versa.

Holographic entanglement entropy probe on spontaneous symmetry breaking with vector order

We study holographic entanglement entropy in 5-dimensional charged black brane geometry obtained from Einstein-SU(2)Yang-Mills theory defined in asymptotically AdS space. This gravity system undergoes second order phase transition near its critical point, where a spatial component of the Yang-Mills fields appears, which is normalizable mode of the solution. This is known as phase transition between isotropic and anisotropic phases, where in anisotropic phase, SO(3)-isometry(spatial rotation) in bulk geometry is broken down to SO(2) by emergence of the spatial component of Yang-Mills fields, which corresponds to a vector order in dual field theory. We get analytic solutions of holographic entanglement entropies by utilizing the solution of bulk spacetime geometry given in arXiv:1109.4592, where we consider subsystems defined on AdS boundary of which shapes are wide and thin slabs and a cylinder. It turns out that the entanglement entropies near the critical point shows scaling behavior such that for both of the slabs and cylinder, {Delta}_{varepsilon }Ssim {left(1-frac{T}{T_c}right)}^{beta } and the critical exponent β = 1, where ∆εS ≡ Siso− Saniso, and Siso denotes the entanglement entropy in isotropic phase whereas Saniso denotes that in anisotropic phase. We suggest a quantity O12≡ S1− S2 as a new order parameter near the critical point, where S1 is entanglement entropy when the slab is perpendicular to the direction of the vector order whereas S2 is that when the slab is parallel to the vector order. O12 = 0 in isotropic phase but in anisotropic phase, the order parameter becomes non-zero showing the same scaling behavior. Finally, we show that even near the critical point, the first law of entanglement entropy is held. Especially, we find that the entanglement temperature for the cylinder is {mathcal{T}}_{cy}=frac{c_{textrm{ent}}}{a} , where cent = 0.163004 ± 0.000001 and a is the radius of the cylinder.

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.

Holographic study of reflected entropy in anisotropic theories

We evaluate reflected entropy in certain anisotropic boundary theories dual to nonrelativistic geometries using holography. It is proposed that this quantity is proportional to the minimal area of the entanglement wedge cross section. Using this prescription, we study in detail the effect of anisotropy on reflected entropy and other holographic entanglement measures. In particular, we study the discontinuous phase transition of this quantity for a symmetric configuration consisting of two disjoint strips. We find that in the specific regimes of the parameter space the critical separation is an increasing function of the anisotropy parameter and hence the correlation between the subregions becomes more pronounced. We carefully examine how these results are consistent with the behavior of other correlation measures including the mutual information. Finally, we show that the structure of the universal terms of entanglement entropy is corrected depending on the orientation of the entangling region with respect to the anisotropic direction.

Pseudoentropy in dS/CFT and Timelike Entanglement Entropy.

We study holographic entanglement entropy in dS/CFT and introduce timelike entanglement entropy in CFTs. Both of them take complex values in general and are related with each other via an analytical continuation. We argue that they are correctly understood as pseudoentropy. We find that the imaginary part of pseudoentropy implies an emergence of time in dS/CFT.

Holographic entanglement entropy of the double Wick rotated BTZ black hole

In this paper, we analyze the holographic covariant entanglement entropy in the double Wick rotated version of a rotating BTZ black hole (3 dimensional Kerr-AdS solution), where the periodicity of Euclidean time and spatial direction are changed. The dual field theory has negative energy in the Lorentzian signature. The holographic entanglement entropy agrees with its CFT counterpart, which is obtained by a conformal transformation of the correlation functions of twisted operators.

Wedge holography in flat space and celestial holography

In this paper, we study codimension two holography in flat spacetimes, based on the idea of the wedge holography. We propose that a region in a $d+1$ dimensional flat spacetime surrounded by two end of the world-branes, which are given by $d$ dimensional hyperbolic spaces, is dual to a conformal field theory (CFT) on a $d-1$ dimensional sphere. Similarly, we also propose that a $d+1$ dimensional region in the flat spacetime bounded by two $d$ dimensional de Sitter spaces is holographically dual to a CFT on a $d-1$ dimensional sphere. Our calculations of the partition function, holographic entanglement entropy and two point functions, support these duality relations and imply that such CFTs are non-unitary. Finally, we glue these two dualities along null surfaces to realize a codimension two holography for a full Minkowski spacetime and discuss a possible connection to the celestial holography.

Holographic BCFT with a Defect on the End-of-the-World brane

In this paper, we propose a new gravity dual for a 2d BCFT with two conformal boundaries by introducing a defect that connects the two End-of-the-World branes. We demonstrate that the BCFT dual to this bulk model exhibits a richer lowest spectrum. The corresponding lowest energy eigenvalue can continuously interpolate between -frac{pi c}{24Delta x} and 0 where ∆x is the distance between the boundaries. This range was inaccessible to the conventional AdS/BCFT model with distinct boundary conditions. We compute the holographic entanglement entropy and find that it exhibits three different phases, one of which breaks the time reflection symmetry. We also construct a wormhole saddle, analogous to a 3d replica wormhole, which connects different boundaries through the AdS bulk. This saddle is present only if the BCFT is non-unitary and is always subdominant compared to the disconnected saddle.

CFT correlators from shape deformations in Cubic Curvature Gravity

We find a covariant expression for the universal part of the holographic entanglement entropy which is valid for CFTs dual to generic higher curvature gravities in up to five bulk dimensions. We use this functional to compute universal coefficients of stress-tensor correlators in three-dimensional CFTs dual to Cubic Curvature Gravity. Using gauge/gravity duality, we work out an expression for the entanglement entropy of deformed entangling regions and read the coefficients from the power expansion of the entropy in the deformation parameter. In particular, we obtain the t4 coefficient of the 3-point function and exhibit a difference between the results obtained using the entanglement entropy functional for minimal and non-minimal splittings. We compare the obtained expressions for t4 derived considering both splittings with results obtained through other holographic methods which are splitting-independent. We find agreement with the result obtained from the non-minimal splitting, whereas the result derived from the minimal splitting is inconsistent and it is therefore ruled out.

Holographic entanglement entropy inequalities beyond strong subadditivity

The vacuum entanglement entropy in quantum field theory provides nonperturbative information about renormalization group flows. Most studies so far have focused on the universal terms, related to the Weyl anomaly in even space-time dimensions, and the sphere free energy F in odd dimensions. In this work we study the entanglement entropy on a sphere of radius R in a large radius limit, for field theories with gravity duals. At large radius the entropy admits a geometric expansion in powers of R; the leading term is the well-known area term, and we also consider the subleading contributions. These terms can be physical, they contain information about the full renormalization group flow, and they reproduce known monotonicity theorems in particular cases. We set up an efficient method for calculating them using the Hamilton-Jacobi equation for the holographic entanglement entropy. We first reproduce the known result for the area term, the coefficient multiplying Rd−2 in the entanglement entropy. We then obtain the holographic result for the Rd−4 term and establish its irreversibility. Finally, we derive the Rd−6 coefficient for holographic theories, and also establish its irreversibility. This result goes beyond what has been proved in quantum field theory based on strong subadditivity, and hints towards new methods for analyzing the monotonicity of the renormalization group in space-time dimensions bigger than four.

Holographic tensor networks from hyperbolic buildings

We introduce a unifying framework for the construction of holographic tensor networks, based on the theory of hyperbolic buildings. The underlying dualities relate a bulk space to a boundary which can be homeomorphic to a sphere, but also to more general spaces like a Menger sponge type fractal. In this general setting, we give a precise construction of a large family of bulk regions that satisfy complementary recovery. For these regions, our networks obey a Ryu-Takayanagi formula. The areas of Ryu-Takayanagi surfaces are controlled by the Hausdorff dimension of the boundary, and consistently generalize the behavior of holographic entanglement entropy in integer dimensions to the non-integer case. Our construction recovers HaPPY-like codes in all dimensions, and generalizes the geometry of Bruhat-Tits trees. It also provides examples of infinite-dimensional nets of holographic conditional expectations, and opens a path towards the study of conformal field theory and holography on fractal spaces.

Extremal surfaces and thin-shell wormholes

We study extremal surfaces in a traversable wormhole geometry that connects two locally ${\mathrm{AdS}}_{5}$ asymptotic regions. In the context of the $\mathrm{AdS}/\mathrm{CFT}$ correspondence, we use these to compute the holographic entanglement entropy for different configurations: First, we consider an extremal surface anchored at the boundary on a spatial 2-sphere of radius $R$. The other scenario is a slab configuration which extends in two of the boundary spacelike directions while having a finite size $L$ in the third one. We show that in both cases the divergent and the finite pieces of the holographic entanglement entropy give results consistent with the holographic picture and this is used to explore the phase transitions that the dual theory undergoes. The geometries we consider here are stable thin-shell wormholes with flat codimension-one hypersurfaces at fixed radial coordinate. They appear as electrovacuum solutions of higher-curvature gravity theories coupled to Abelian gauge fields. The presence of the thin shells produces a refraction of the extremal surfaces in the bulk, leading to the presence of cusps in the phase space diagram. Further, the traversable wormhole captures a phase transition for the subsystems made up of a union of disconnected regions in different boundaries. We discuss these and other features of the phase diagram.

Upper bounds of holographic entanglement entropy growth rate for thermofield double states

We studied the upper bounds of the holographic entanglement entropy growth rate for thermofield double (TFD) states. By comparing the cases of vacuum AdS and charged AdS black holes, we conjecture: for all static planar or spherically symmetric asymptotically Schwarzschild-AdS black holes of same mass density or entropy density, the vacuum AdS black hole gives the maximum entanglement entropy growth rate. We gave proofs by assuming dominant energy condition. We also considered the AdS black hole spacetime with real scalar fields case, where the scalar fields violate the dominant energy condition and the bulk geometry is not asymptotically Schwarzschild-AdS. Numerical results show that this case vacuum black hole still has maximal growth rate if we fixed entropy. However, in the case of fixed energy, vacuum case has maximal growth rate of entanglement entropy only under standard quantization scheme.

Noncommutative Corrections to the Minimal Surface Areas of the Pure AdS Spacetime and Schwarzschild-AdS Black Hole

Based on the perturbation expansion, we compute the noncommutative corrections to the minimal surface areas of the pure AdS spacetime and Schwarzschild-AdS black hole, where the noncommutative background is suitably constructed in terms of the Poincaré coordinate system. In particular, we find a reasonable tetrad with subtlety, which not only matches the metrics of the pure AdS spacetime and Schwarzschild-AdS black hole in the commutative case, but also makes the corrections real rather than complex in the noncommutative case. For the pure AdS spacetime, the nocommutative effect is only a logarithmic term, while for the Schwarzschild-AdS black hole, it contains a logarithmic contribution plus both a mass term and a noncommutative parameter related term. Furthermore, we show that the holographic entanglement entropy with noncommutativity obeys a relation which is similar to the first law of thermodynamics in the pure AdS spacetime.

Perfect tensor hyperthreads

Bit threads, a dual description of the Ryu-Takyanagi formula for holographic entanglement entropy (EE), can be interpreted as a distillation of the quantum information to a collection of Bell pairs between different boundary regions. In this article we discuss a generalization to hyperthreads which can connect more than two boundary regions leading to a rich and diverse class of convex programs. By modeling the contributions of different species of hyperthreads to the EEs of perfect tensors we argue that this framework may be useful for helping us to begin to probe the multipartite entanglement of holographic systems. Furthermore, we demonstrate how this technology can potentially be used to understand holographic entropy cone inequalities and may provide an avenue to address issues of locking.