A class of (2+1)-dimensional quantum many body system characterized by an anisotropic scaling symmetry (Lifshitz symmetry) near their quantum critical point can be described by a (3+1)-dimensional dual gravity theory with negative cosmological constant along with a massive vector field, where the scaling symmetry is realized by the metric as an isometry. We calculate the entanglement entropy of an excited state of such a system holographically, i.e., from the asymptotic perturbation of the gravity dual using the prescription of Ryu and Takayanagi, when the subsystem is sufficiently small. With suitable identifications, we show that this entanglement entropy satisfies an energy conservation relation analogous to the first law of thermodynamics. The non-trivial massive vector field here plays a crucial role and contributes to an additional term in the energy relation.

In this paper, we have studied the holographic subregion complexity for boosted black brane for strip like subsystem. The holographic subregion complexity has been computed for a subsystem chosen along and perpendicular to the boost direction. We have observed that there is an asymmetry in the result due to the boost parameter which can be attributed to the asymmetry in the holographic entanglement entropy. The Fisher information metric and the fidelity susceptibility have also been computed using bulk dual prescriptions. It is observed that the two metrics computed holographically are not related for both the pure black brane as well as the boosted black brane. This is one of the main findings in this paper and the holographic results have been compared with the results available in the quantum information literature where it is known that the two distances are related to each other in

In this paper, we compute the exact form of the bulk geometry emerging from a (1 + 1)-dimensional conformal field theory using the holographic principle. We first consider the (2 + 1)-dimensional asymptotic AdS metric in Poincare coordinates and compute the area functional corresponding to the static minimal surface γ A and obtain the entanglement entropy making use of the holographic entanglement entropy proposal. We then use the results of the entanglement entropy for (1 + 1)dimensional conformal field theory on an infinite line, on an infinite line at a finite temperature and on a circle. Comparing these results with the holographic entanglement entropy, we are able to extract the proper structure of the bulk metric. Finally, we also carry out our analysis in the case of N = 4 super Yang-Mills theory and obtain the exact form of the dual bulk geometry corresponding to this theory. The analysis reveals the behavior of the bulk metric in both the near boundary region and deep inside the bulk. The results also show the influence of the boundary UV cut-off "a" on the bulk metric. It is observed that the reconstructed metrics match exactly with the known results in the literature when one moves deep inside the bulk or towards the turning point. *

The subregion holographic complexity of a 3 þ 1-dimensional Lifshitz spacetime having a scaling symmetry is computed. The change in the holographic complexity between the excited state and the ground state is then obtained. It is found that there is a nontrivial change in holographic complexity at first order in the perturbation of the pure Lifshitz geometry. The difference is next related to the changes in the energy and the entanglement chemical potential of the system. The calculation is carried out for both the values of the dynamical scaling exponent z in the Lifshitz spacetime. The relations have a very similar form to the corresponding relation involving the change in entanglement entropy known to be an analogous relation to the first law of thermodynamics.