Entanglement entropy of an annulus in holographic thermalization

The thermalization process of the holographic entanglement entropy(HEE)of an annular domain is investigated in the Vaidya-AdS geometry.We determine numerically the Hubeny-Rangamani-Takayanagi(HRT)surface,which may be a hemi-torus or two disks,depending on the ratio of the inner radius to the outer radius of the annulus.More importantly,for some fixed ratio of the two radii,the annulus undergoes a phase transition,or a double phase transition,during thermalization from a hemi-torus to a two-disk configuration,or vice versa.The occurrence of various phase transitions is determined by the ratio of the two radii of the annulus.The rate of entanglement growth is also investigated during the thermal quench.The local maximal rate of entanglement growth occurs in the region with a double phase transition.Finally,if the quench process is sufficiently slow,which may be controlled by the thickness of the null shell,the region with a double phase transition vanishes.     

Power-Law entropy corrected holographic dark energy model

Among various scenarios to explain the acceleration of the universe expansion, the holographic dark energy (HDE) model has got a lot of enthusiasm recently. In the derivation of holographic energy density, the area relation of the black hole entropy plays a crucial role. Indeed, the power-law corrections to entropy appear in dealing with the entanglement of quantum fields in and out the horizon. Inspired by the power-law corrected entropy, we propose the so-called “power-law entropy-corrected holographic dark energy” (PLECHDE) in this Letter. We investigate the cosmological implications of this model and calculate some relevant cosmological parameters and their evolution. We also briefly study the so-called “power-law entropy-corrected agegraphic dark energy” (PLECADE).     

Entanglement in holographic dark energy models

We study a process of equilibration of holographic dark energy (HDE) with the cosmic horizon around the dark-energy dominated epoch. This process is characterized by a huge amount of information conveyed across the horizon, filling thereby a large gap in entropy between the system on the brink of experiencing a sudden collapse to a black hole and the black hole itself. At the same time, even in the absence of interaction between dark matter and dark energy, such a process marks a strong jump in the entanglement entropy, measuring the quantum-mechanical correlations between the horizon and its interior. Although the effective quantum field theory (QFT) with a peculiar relationship between the UV and IR cutoffs, a framework underlying all HDE models, may formally account for such a huge shift in the number of distinct quantum states, we show that the scope of such a framework becomes tremendously restricted, devoid virtually any application in other cosmological epochs or particle-physics phenomena. The problem of negative entropies for the non-phantom stuff is also discussed.     

Entanglement entropy in Abelian gauge theories

The definition of geometric entanglement entropy associated with some region in space is discussed for the case of gauge theories. It is argued that since in gauge theories elementary excitations look like loops (closed electric strings) rather than points (particles), the boundaries of the regions should also carry some nonzero entropy. This entropy counts the number of strings which cross these boundaries. Explicit calculations of such entropy are carried out in the limits of infinitely strong and weak couplings of three- and four-dimensional Z _N gauge theories. In three dimensions we find that the entropy is a constant which does not depend on the region, while in four dimensions the familiar area law for the entropy is recovered.     

Entanglement entropy in extended quantum systems

After a brief introduction to the concept of entanglement in quantum systems, I apply these ideas to many-body systems and show that the von Neumann entropy is an effective way of characterising the entanglement between the degrees of freedom in different regions of space. Close to a quantum phase transition it has universal features which serve as a diagnostic of such phenomena. In the second part I consider the unitary time evolution of such systems following a ‘quantum quench’ in which a parameter in the Hamiltonian is suddenly changed, and argue that finite regions should effectively thermalise at late times, after interesting transient effects.     

Entanglement entropy in fermionic Laughlin states

We present analytic and numerical calculations on the bipartite entanglement entropy in fractional quantum Hall states of the fermionic Laughlin sequence. The partitioning of the system is done both by dividing Landau-level orbitals and by grouping the fermions themselves. For the case of orbital partitioning, our results can be related to spatial partitioning, enabling us to extract a topological quantity (the "total quantum dimension") characterizing the Laughlin states. For particle partitioning we prove a very close upper bound for the entanglement entropy of a subset of the particles with the rest, and provide an interpretation in terms of exclusion statistics.     

Entanglement entropy of one-dimensional gases

We introduce a systematic framework to calculate the bipartite entanglement entropy of a spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. To show the wide range of applicability of the proposed formalism, we use it for the calculation of the entanglement in the eigenstates of periodic systems, in a gas confined by boundaries or external potentials, in junctions of quantum wires, and in a time-dependent parabolic potential.     

Entanglement entropy of round spheres

We propose that the logarithmic term in the entanglement entropy computed in a conformal field theory for a (d−2)$(d-2)$-dimensional round sphere in Minkowski spacetime is identical to the logarithmic term in the entanglement entropy of extreme black hole. The near horizon geometry of the latter is H₂×S_d−2$H_2\times S_{d-2}$. For a scalar field this proposal is checked by direct calculation. We comment on relation of this and earlier calculations to the “brick wall” model of 't Hooft. The case of generic 4d conformal field theory is discussed.     

Entanglement switching via the Kondo effect in triple quantum dots

We consider a triple quantum dot system in a triangular geometry with one of the dots connected to metallic leads. Using Wilson’s numerical renormalization group method, we investigate quantum entanglement and its relation to the thermodynamic and transport properties in the regime where each of the dots is singly occupied on average, but with non-negligible charge fluctuations. It is shown that even in the regime of significant charge fluctuations the formation of the Kondo singlets induces switching between separable and perfectly entangled states. The quantum phase transition between unentangled and entangled states is analyzed quantitatively and the corresponding phase diagram is explained by exactly solvable spin model. In the framework of an effective model we also explain smearing of the entanglement transition for cases when the symmetry of the triple quantum dot system is relaxed.     

Entanglement entropy converges to classical entropy around periodic orbits

We consider oscillators evolving subject to a periodic driving force that dynamically entangles them, and argue that this gives the linearized evolution around periodic orbits in a general chaotic Hamiltonian dynamical system. We show that the entanglement entropy, after tracing over half of the oscillators, generically asymptotes to linear growth at a rate given by the sum of the positive Lyapunov exponents of the system. These exponents give a classical entropy growth rate, in the sense of Kolmogorov, Sinai and Pesin. We also calculate the dependence of this entropy on linear mixtures of the oscillator Hilbert-space factors, to investigate the dependence of the entanglement entropy on the choice of coarse graining. We find that for almost all choices the asymptotic growth rate is the same.     

Entanglement entropy fluctuations in quantum Ising chains

The behavior of Ising chains with the spin-spin interaction value λ in a transverse magnetic field of constant intensity (h = 1) is considered. For a chain of infinite length, exact analytical formulas are obtained for the second central moment (dispersion) of the entropy operator Ŝ = -lnρ with reduced density matrix ρ, which corresponds to a semi-infinite part of the model chain occurring in the ground state. In the vicinity of a critical point λ_c = 1, the entanglement entropy fluctuation ΔS (defined as the square root of dispersion) diverges as ΔS ∼ [ln(1/|1 − λ|)]^1/2. For the known behavior of the entanglement entropy S, this divergence results in that the relative fluctuation δS = ΔS/S vanishes at the critical point, that is, a state with almost nonfluctuating entanglement is attained.