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.Comment: 6 pages. Plenary talk delivered at Statphys 23, Genoa, July 200

Entanglement entropy of two disjoint intervals in conformal field theory

We study the entanglement of two disjoint intervals in the conformal field theory of the Luttinger liquid (free compactified boson). Tr\rho_A^n for any integer n is calculated as the four-point function of a particular type of twist fields and the final result is expressed in a compact form in terms of the Riemann-Siegel theta functions. In the decompactification limit we provide the analytic continuation valid for all model parameters and from this we extract the entanglement entropy. These predictions are checked against existing numerical data.Comment: 34 pages, 7 figures. V2: Results for small x behavior added, typos corrected and refs adde

On entanglement evolution across defects in critical chains

We consider a local quench where two free-fermion half-chains are coupled via a defect. We show that the logarithmic increase of the entanglement entropy is governed by the same effective central charge which appears in the ground-state properties and which is known exactly. For unequal initial filling of the half-chains, we determine the linear increase of the entanglement entropy.Comment: 11 pages, 5 figures, minor changes, reference adde

Observations Outside the Light-Cone: Algorithms for Non-Equilibrium and Thermal States

We apply algorithms based on Lieb-Robinson bounds to simulate time-dependent and thermal quantities in quantum systems. For time-dependent systems, we modify a previous mapping to quantum circuits to significantly reduce the computer resources required. This modification is based on a principle of "observing" the system outside the light-cone. We apply this method to study spin relaxation in systems started out of equilibrium with initial conditions that give rise to very rapid entanglement growth. We also show that it is possible to approximate time evolution under a local Hamiltonian by a quantum circuit whose light-cone naturally matches the Lieb-Robinson velocity. Asymptotically, these modified methods allow a doubling of the system size that one can obtain compared to direct simulation. We then consider a different problem of thermal properties of disordered spin chains and use quantum belief propagation to average over different configurations. We test this algorithm on one dimensional systems with mixed ferromagnetic and anti-ferromagnetic bonds, where we can compare to quantum Monte Carlo, and then we apply it to the study of disordered, frustrated spin systems.Comment: 19 pages, 12 figure

The One-dimensional KPZ Equation and the Airy Process

Our previous work on the one-dimensional KPZ equation with sharp wedge initial data is extended to the case of the joint height statistics at n spatial points for some common fixed time. Assuming a particular factorization, we compute an n-point generating function and write it in terms of a Fredholm determinant. For long times the generating function converges to a limit, which is established to be equivalent to the standard expression of the n-point distribution of the Airy process.Comment: 15 page

Field-theory results for three-dimensional transitions with complex symmetries

We discuss several examples of three-dimensional critical phenomena that can be described by Landau-Ginzburg-Wilson $\phi^4$ theories. We present an overview of field-theoretical results obtained from the analysis of high-order perturbative series in the frameworks of the $\epsilon$ and of the fixed-dimension d=3 expansions. In particular, we discuss the stability of the O(N)-symmetric fixed point in a generic N-component theory, the critical behaviors of randomly dilute Ising-like systems and frustrated spin systems with noncollinear order, the multicritical behavior arising from the competition of two distinct types of ordering with symmetry O($n_1$) and O($n_2$) respectively.Comment: 9 pages, Talk at the Conference TH2002, Paris, July 200

An aging evaluation of the bearing performances of glass fiber composite laminate in salt spray fog environment

The aim of the present paper is to assess the bearing performance evolution of pinned, glass-composite laminates due to environmental aging in salt-spray fog tests. Glass fibers/epoxy pinned laminates were exposed for up to 60 days in salt-spraying, foggy environmental conditions (according to ASTM B117 standard). In order to evaluate the relationship between mechanical failure mode and joint stability over increasing aging time, different single lap joints, measured by the changing hole diameter (D), laminate width (W) and hole free edge distance (E), were characterized at varying aging steps. Based on this approach, the property-structure relationship of glass-fibers/epoxy laminates was assessed under these critical environmental conditions. Furthermore, an experimental 2D failure map, clustering main failure modes in the plane E/D versus W/D ratios, was generated, and its cluster variation was analyzed at each degree of aging

Entanglement Dynamics after a Quench in Ising Field Theory: A Branch Point Twist Field Approach

We extend the branch point twist field approach for the calculation of entanglement entropies to time-dependent problems in 1+1-dimensional massive quantum field theories. We focus on the simplest example: a mass quench in the Ising field theory from initial mass m0 to final mass m. The main analytical results are obtained from a perturbative expansion of the twist field one-point function in the post-quench quasi-particle basis. The expected linear growth of the Rényi entropies at large times mt ≫ 1 emerges from a perturbative calculation at second order. We also show that the Rényi and von Neumann entropies, in infinite volume, contain subleading oscillatory contributions of frequency 2m and amplitude proportional to (mt)−3/2. The oscillatory terms are correctly predicted by an alternative perturbation series, in the pre-quench quasi-particle basis, which we also discuss. A comparison to lattice numerical calculations carried out on an Ising chain in the scaling limit shows very good agreement with the quantum field theory predictions. We also find evidence of clustering of twist field correlators which implies that the entanglement entropies are proportional to the number of subsystem boundary points

Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?

We study the time evolution of quantum one-dimensional gapless systems evolving from initial states with a domain-wall. We generalize the path-integral imaginary time approach that together with boundary conformal field theory allows to derive the time and space dependence of general correlation functions. The latter are explicitly obtained for the Ising universality class, and the typical behavior of one- and two-point functions is derived for the general case. Possible connections with the stochastic Loewner evolution are discussed and explicit results for one-point time dependent averages are obtained for generic \kappa for boundary conditions corresponding to SLE. We use this set of results to predict the time evolution of the entanglement entropy and obtain the universal constant shift due to the presence of a domain wall in the initial state.Comment: 27 pages, 10 figure