Entanglement entropy and D1-D5 geometries

http://dx.doi.org/10.1103/PhysRevD.90.066004Giusto, Stefano, and Rodolfo Russo. "Entanglement Entropy and D1-D5 geometries." Physical Review D 90.6 (2014): 066004

Entanglement entropy and quantum field theory: a non-technical introduction

In these proceedings we give a pedagogical and non-technical introduction to the Quantum Field Theory approach to entanglement entropy. Particular attention is devoted to the one space dimensional case, with a linear dispersion relation, that, at a quantum critical point, can be effectively described by a two-dimensional Conformal Field Theory.Comment: 10 Pages, 2 figures. Talk given at the conference "Entanglement in Physical and information sciences", Centro Ennio de Giorgi, Pisa, December 200

A class of quantum many-body states that can be efficiently simulated

We introduce the multi-scale entanglement renormalization ansatz (MERA), an efficient representation of certain quantum many-body states on a D-dimensional lattice. Equivalent to a quantum circuit with logarithmic depth and distinctive causal structure, the MERA allows for an exact evaluation of local expectation values. It is also the structure underlying entanglement renormalization, a coarse-graining scheme for quantum systems on a lattice that is focused on preserving entanglement.Comment: 4 pages, 5 figure

Ageing Properties of Critical Systems

In the past few years systems with slow dynamics have attracted considerable theoretical and experimental interest. Ageing phenomena are observed during this ever-lasting non-equilibrium evolution. A simple instance of such a behaviour is provided by the dynamics that takes place when a system is quenched from its high-temperature phase to the critical point. The aim of this review is to summarize the various numerical and analytical results that have been recently obtained for this case. Particular emphasis is put to the field-theoretical methods that can be used to provide analytical predictions for the relevant dynamical quantities. Fluctuation-dissipation relations are discussed and in particular the concept of fluctuation-dissipation ratio (FDR) is reviewed, emphasizing its connection with the definition of a possible effective temperature. The Renormalization-Group approach to critical dynamics is summarized and the scaling forms of the time-dependent non-equilibrium correlation and response functions of a generic observable are discussed. From them the universality of the associated FDR follows as an amplitude ratio. It is then possible to provide predictions for ageing quantities in a variety of different models. In particular the results for Model A, B, and C dynamics of the O(N) Ginzburg-Landau Hamiltonian, and Model A dynamics of the weakly dilute Ising magnet and of a \phi^3 theory, are reviewed and compared with the available numerical results and exact solutions. The effect of a planar surface on the ageing behaviour of Model A dynamics is also addressed within the mean-field approximation.Comment: rvised enlarged version, 72 Pages, Topical Review accepted for publication on JP

Unusual Corrections to Scaling in Entanglement Entropy

We present a general theory of the corrections to the asymptotic behaviour of the Renyi entropies which measure the entanglement of an interval A of length L with the rest of an infinite one-dimensional system, in the case when this is described by a conformal field theory of central charge c. These can be due to bulk irrelevant operators of scaling dimension x>2, in which case the leading corrections are of the expected form L^{-2(x-2)} for values of n close to 1. However for n>x/(x-2) corrections of the form L^{2-x-x/n} and L^{-2x/n} arise and dominate the conventional terms. We also point out that the last type of corrections can also occur with x less than 2. They arise from relevant operators induced by the conical space-time singularities necessary to describe the reduced density matrix. These agree with recent analytic and numerical results for quantum spin chains. We also compute the effect of marginally irrelevant bulk operators, which give a correction (log L)^{-2}, with a universal amplitude. We present analogous results for the case when the interval lies at the end of a semi-infinite system.Comment: 15 pages, no figure