Narrow Results

We show that boundedness of entanglement entropy for pure states of bipartite quantum spin systems implies split property of subsystems. As a corollary, in one-dimensional quantum spin chains, we show that the split property with respect to left and right semi-infinite subsystems is valid for the translationally invariant pure ground states with spectral gap.

In this comprehensive study of Kitaev’s abelian models defined on a graph embedded on a closed orientable surface, we provide complete proofs of the topological ground state degeneracy, the absence of local order parameters, compute the entanglement entropy exactly and characterize the elementary anyonic excitations. The homology and cohomology groups of the cell complex play a central role and allow for a rigorous understanding of the relations between the above characterizations of topological order.

We locate the relevant degrees of freedom for the entanglement entropy on some 2+1 fuzzy models. It is found that the entropy is stored in the near boundary degrees of freedom. We give a simple analytical derivation for the area law using 1/N like expansion when only the near boundary degrees of freedom are incorporated. Numerical and qualitative evidences for the validity of near boundary approximation are finally given.

The entropic gravity scenario recently proposed by Erik Verlinde reproduced Newton's law of purely classical gravity yet the key assumptions of this approach all have quantum mechanical origins. As is typical for emergent phenomena in physics, the underlying, more fundamental physics often reveals itself as corrections to the leading classical behavior. So one naturally wonders: where is ℏ hiding in entropic gravity? To address this question, we first revisit the idea of holographic screen as well as entropy and its variation law in order to obtain a self-consistent approach to the problem. Next we argue that since the concept of minimal length has been invoked in the Bekenstein entropic derivation, the generalized uncertainty principle (GUP), which is a direct consequence of the minimal length, should be taken into consideration in the entropic interpretation of gravity. Indeed based on GUP it has been demonstrated that the black hole Bekenstein entropy area law must be modified not only in the strong but also in the weak gravity regime where in the weak gravity limit the GUP modified entropy exhibits a logarithmic correction. When applying it to the entropic interpretation, we demonstrate that the resulting gravity force law does include sub-leading order correction terms that depend on ℏ. Such deviation from the classical Newton's law may serve as a probe to the validity of entropic gravity.

In a dielectric black hole background, photons will be radiated via Hawking evaporation mechanism. In this paper, we calculate the entanglement entropy associated with a static dielectric black hole by employing 't Hooft's brick-wall model. It is found that the lowest energy of radiated particles is coordinate dependent. The resulted entanglement entropy is composed of three parts: a parameter independent leading constant term , a logarithmic correction term and some series terms. The convergency of the series terms is also discussed.

Based on the works of Ghosh et al. who view the black hole entropy as the logarithm of the number of quantum states on the Quantum Isolated Horizon (QIH), the entropy of d-dimensional black hole is studied. According to the Unruh–Verlinde temperature deduced from the concept of entropic force, the statistical entropy of quantum fields under the background of d-dimensional spacetime is calculated by means of quantum statistics. The results reveal the relation between the entanglement entropy of black hole and the logarithm of the number of quantum states and display the effects of dimensions on the correction terms of the entanglement entropy.

Entanglement temperature is an interesting quantity which relates the increased amount of entanglement entropy to that of energy for a weakly excited state in the first-law of entanglement entropy, it is proportional to the inverse of the size of entanglement subsystem and only depends on the shape of the entanglement region. We find the explicit formula of entanglement temperature for the general hyperscaling violation backgrounds with a strip-subsystem. We then investigate the entanglement temperature for a round ball-subsystem, we check that the entanglement temperature has a universal form when the hyperscaling violation exponent is near zero.

A metric is proposed to explore the noncommutative form of the anti-de Sitter (AdS) space due to quantum effects. It has been proved that the noncommutativity in AdS space induces a single component gravitoelectric field. The holographic Ryu–Takayanagi (RT) algorithm is then applied to compute the entanglement entropy (EE) in dual CFT₂. This calculation can be exploited to compute ultraviolet–infrared (UV–IR) cutoff dependent central charge of the certain noncommutative CFT₂. This noncommutative computation of the EE can be interpreted in the form of the surface/state correspondence. We have shown that noncommutativity increases the dimension of the effective Hilbert space of the dual conformal field theory (CFT).

We consider backreacted $Ad{S}_5\times S^5$ coupled with $N_f$ massive flavors introduced by D7 branes. The backreacted geometry is in the Veneziano limit with fixed $N_f/N_c$. By dividing one of the directions into a line segment with length l, we get two subspaces. Then we calculate the entanglement entropy between them. With the method of [I. R. Klebanov, D. Kutasov and A. Murugan, Nucl. Phys. B796, 274 (2008)], we are able to find the cut-off independent part of the entanglement entropy and finally find that this geometry shows no confinement/deconfinement phase transition at zero temperature from the holographic entanglement entropy point of view similar to the case in pure $Ad{S}_5\times S^5$.

Single-particle entanglement entropy (SPEE) is calculated for entanglement Hamiltonian eigenmode in a one-dimensional free fermion model that undergoes a delocalized–localized phase transition. In this numerical study, we show that SPEE of entanglement Hamiltonian eigenmode has the same behavior as SPEE of Hamiltonian eigenmode at the Fermi level: as we go from delocalized phase toward localized phase, SPEE of both modes decrease in the same manner. Furthermore, fluctuations of SPEE of entanglement Hamiltonian eigenmode — which can be obtained through the calculation of moments of SPEE — signature very sharply the phase transition point. These two modes are also compared by calculation of single-particle Rényi entropy (SPRE). We show that SPEE and SPRE of entanglement Hamiltonian eigenmode can be used as phase detection parameters.

We study the entanglement entropy of harmonic oscillators in non-commutative phase space (NCPS). We propose a new definition of quantum Rényi entropy based on Wigner functions in NCPS. Using the Rényi entropy, we calculate the entanglement entropy of the ground state of the 2D isotropic harmonic oscillators. We find that for some values of the non-commutative parameters, the harmonic oscillators can be entangled in NCPS. This is a new entanglement-like effect caused by the non-commutativity of the phase space.

In order to quantize systems involving second-class constraints, one should use Dirac bracket instead of Poisson bracket. Furthermore, one can specify a star product in which the term linear in $\hslash$ is proportional to the Dirac bracket. In this way an oscillator system in a deformed fermionic phase space is analyzed and the corresponding energy level and Wigner functions are evaluated according to scheme of deformation quantization. We also study the entanglement entropy induced by the deformation of the fermionic phase space.

This study investigates the entanglement properties of disordered free fermion systems undergoing an Anderson phase transition from a delocalized to a localized phase. The entanglement entropy is employed to quantify the degree of entanglement, with the system randomly divided into two subsystems. To explore this phenomenon, one-dimensional tight-binding fermion models and Anderson models in one, two, and three dimensions are utilized. Comprehensive numerical calculations reveal that the entanglement entropy, determined using random bi-partitioning, follows a volume-law scaling in both the delocalized and localized phases, expressed as $\mathrm{\text{EE}}\propto L^D$, where D represents the dimension of the system. Furthermore, the role of short and long-range correlations in the entanglement entropy and the impact of the distribution of subsystem sites are analyzed.

By using the entanglement entropy method, the statistical entropy of the Bose and Fermi fields in a thin film is calculated and the Bekenstein–Hawking entropy of Kerr–Newman black hole is obtained. Here, the Bose and Fermi fields are entangled with the quantum states in Kerr–Newman black hole and are outside of the horizon. The divergence of brick-wall model is avoided without any cutoff by the new equation of state density obtained with the generalized uncertainty principle. The calculation implies that the high density quantum states near the event horizon are strongly correlated with the quantum states in black hole. The black hole entropy is a quantum effect. It is an intrinsic characteristic of space–time. The ultraviolet cutoff in the brick-wall model is unreasonable. The generalized uncertainty principle should be considered in the high energy quantum field near the event horizon. From the calculation, the constant λ introduced in the generalized uncertainty principle is related to polar angle θ in an axisymmetric space–time.

We holographically derive entropy of (near) extremal black holes as entanglement entropy of conformal quantum mechanics(CQM) living in two boundaries of AdS₂.

Using a holographic proposal for the entanglement entropy we study its behavior in various supergravity backgrounds. We are particularly interested in the possibility of using the entanglement entropy as way to detect transitions induced by the presence horizons. We consider several geometries with horizons: the black hole in AdS₃, nonextremal Dp-branes, dyonic black holes asymptotically to AdS₄ and also Schwarzschild black holes in global AdS_p coordinates. Generically, we find that the entanglement entropy does not exhibit a transition, that is, one of the two possible configurations always dominates.

Using a holographic proposal for the geometric entropy we study its behavior in the geometry of Schwarzschild black holes in global AdS_p for p = 3, 4, 5. Holographically, the entropy is determined by a minimal surface. On the gravity side, due to the presence of a horizon on the background, generically there are two solutions to the surfaces determining the entanglement entropy. In the case of AdS₃, the calculation reproduces precisely the geometric entropy of an interval of length l in a two-dimensional conformal field theory with periodic boundary conditions. We demonstrate that in the cases of AdS₄ and AdS₅ the sign of the difference of the geometric entropies changes, signaling a transition. Euclideanization implies that various embedding of the holographic surface are possible. We study some of them and find that the transitions are ubiquitous. In particular, our analysis renders a very intricate phase space, showing, for some ranges of the temperature, up to three branches. We observe a remarkable universality in the type of results we obtain from AdS₄ and AdS₅.

In this paper, we will explain an application of holographic entanglement entropy to Fermi surface physics. These holographic arguments show that Landau–Fermi liquids do not have any gravity duals in the purely classical limit [N. Ogawa, T. Takayanagi and T. Ugajin, J. High Energy Phys.125, 1 (2012), arXiv:1111.1023 [hep-th]].

In Schwinger effect, quantum vacuum instability under the influence of an electric field leads to decay of vacuum into pairs of charged particles. We consider the entanglement of pair produced particles. We will show that the measure of entanglement depends on the geometry of space–time. Using the Schwinger pair production in curved space–time, dS₂ and AdS₂, we propose and demonstrate that the electric field can generate entanglement. In dS₂ space–time, we study entanglement for scalar particles with zero spin in the absence and presence of a constant electric field. We show that the entanglement entropy depends on the choice of the α-vacua. But, for some values of the related parameters (mass, charge, scalar curvature, electric field), the entanglement entropy is independent of α. Also, we consider the generation of entanglement in the presence of a constant electric field for anti-de Sitter space–time. We will show that the positive (negative) curvature of space–time upgrades (degrades) the generated entanglement.

In this paper, we investigate the entanglement entropy for the generalized charged BTZ black hole through the AdS₃/CFT₂ correspondence. Using the holographic description of the entanglement entropy for the strip-subsystem in boundary CFT₂, we will find the first law-like relation between the variation of holographic entanglement entropy and the variation of energy of the subsystem in terms of the mass and the electric charge up to the second-order. We also obtain appropriate counterterms to renormalize the energy tensor associated with the bulk on-shell actions.