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

Quantum Quench from a Thermal Initial State

We consider a quantum quench in a system of free bosons, starting from a thermal initial state. As in the case where the system is initially in the ground state, any finite subsystem eventually reaches a stationary thermal state with a momentum-dependent effective temperature. We find that this can, in some cases, even be lower than the initial temperature. We also study lattice effects and discuss more general types of quenches.Comment: 6 pages, 2 figures; short published version, added references, minor change

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 versus mutual information in quantum spin chains

The quantum entanglement $E$ of a bipartite quantum Ising chain is compared with the mutual information $I$ between the two parts after a local measurement of the classical spin configuration. As the model is conformally invariant, the entanglement measured in its ground state at the critical point is known to obey a certain scaling form. Surprisingly, the mutual information of classical spin configurations is found to obey the same scaling form, although with a different prefactor. Moreover, we find that mutual information and the entanglement obey the inequality $I\leq E$ in the ground state as well as in a dynamically evolving situation. This inequality holds for general bipartite systems in a pure state and can be proven using similar techniques as for Holevo's bound.Comment: 10 pages, 3 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

Pairing, crystallization and string correlations of mass-imbalanced atomic mixtures in one-dimensional optical lattices

We numerically determine the very rich phase diagram of mass-imbalanced binary mixtures of hardcore bosons (or equivalently -- fermions, or hardcore-Bose/Fermi mixtures) loaded in one-dimensional optical lattices. Focusing on commensurate fillings away from half filling, we find a strong asymmetry between attractive and repulsive interactions. Attraction is found to always lead to pairing, associated with a spin gap, and to pair crystallization for very strong mass imbalance. In the repulsive case the two atomic components remain instead fully gapless over a large parameter range; only a very strong mass imbalance leads to the opening of a spin gap. The spin-gap phase is the precursor of a crystalline phase occurring for an even stronger mass imbalance. The fundamental asymmetry of the phase diagram is at odds with recent theoretical predictions, and can be tested directly via time-of-flight experiments on trapped cold atoms.Comment: 4 pages, 4 figures + Supplementary Materia

Infinite qubit rings with maximal nearest neighbor entanglement: the Bethe ansatz solution

We search for translationally invariant states of qubits on a ring that maximize the nearest neighbor entanglement. This problem was initially studied by O'Connor and Wootters [Phys. Rev. A {\bf 63}, 052302 (2001)]. We first map the problem to the search for the ground state of a spin 1/2 Heisenberg XXZ model. Using the exact Bethe ansatz solution in the limit of an infinite ring, we prove the correctness of the assumption of O'Connor and Wootters that the state of maximal entanglement does not have any pair of neighboring spins ``down'' (or, alternatively spins ``up''). For sufficiently small fixed magnetization, however, the assumption does not hold: we identify the region of magnetizations for which the states that maximize the nearest neighbor entanglement necessarily contain pairs of neighboring spins ``down''.Comment: 10 pages, 4 figures; Eq. (45) and Fig. 3 corrected, no qualitative change in conclusion

Entanglement entropy in gauge theories and the holographic principle for electric strings

We consider quantum entanglement between gauge fields in some region of space A and its complement B. It is argued that the Hilbert space of physical states of gauge theories cannot be decomposed into a direct product of Hilbert spaces of states localized in A and B. The reason is that elementary excitations in gauge theories - electric strings - are associated with closed loops rather than points in space, and there are closed loops which belong both to A and B. Direct product structure and hence the reduction procedure with respect to the fields in B can only be defined if the Hilbert space of physical states is extended by including the states of electric strings which can open on the boundary of A. The positions of string endpoints on this boundary are the additional degrees of freedom which also contribute to the entanglement entropy. We explicitly demonstrate this for the three-dimensional Z2 lattice gauge theory both numerically and using a simple trial ground state wave function. The entanglement entropy appears to be saturated almost completely by the entropy of string endpoints, thus reminding of a ``holographic principle'' in quantum gravity and AdS/CFT correspondence.Comment: 6 pages RevTeX, 5 figure

Free-energy distribution of the directed polymer at high temperature

We study the directed polymer of length $t$ in a random potential with fixed endpoints in dimension 1+1 in the continuum and on the square lattice, by analytical and numerical methods. The universal regime of high temperature $T$ is described, upon scaling 'time' $t \sim T^5/\kappa$ and space $x = T^3/\kappa$ (with $\kappa=T$ for the discrete model) by a continuum model with $\delta$-function disorder correlation. Using the Bethe Ansatz solution for the attractive boson problem, we obtain all positive integer moments of the partition function. The lowest cumulants of the free energy are predicted at small time and found in agreement with numerics. We then obtain the exact expression at any time for the generating function of the free energy distribution, in terms of a Fredholm determinant. At large time we find that it crosses over to the Tracy Widom distribution (TW) which describes the fixed $T$ infinite $t$ limit. The exact free energy distribution is obtained for any time and compared with very recent results on growth and exclusion models.Comment: 6 pages, 3 figures large time limit corrected and convergence to Tracy Widom established, 1 figure changed

Entanglement Entropy of Two Spheres

We study the entanglement entropy S_{AB} of a massless free scalar field on two spheres A and B whose radii are R_1 and R_2, respectively, and the distance between the centers of them is r. The state of the massless free scalar field is the vacuum state. We obtain the result that the mutual information S_{A;B}:=S_A+S_B-S_{AB} is independent of the ultraviolet cutoff and proportional to the product of the areas of the two spheres when r>>R_1,R_2, where S_A and S_B are the entanglement entropy on the inside region of A and B, respectively. We discuss possible connections of this result with the physics of black holes.Comment: 17 pages, 9 figures; v4, added references, revised argument in section V, a typo in eq.(25) corrected, published versio