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In this review, we discuss the zero and finite temperature behavior of various bipartite quantum and total correlation measures, the skew information-based quantum coherence, and the local quantum uncertainty in the thermal ground state of the one-dimensional anisotropic XY model in transverse magnetic field. We compare the ability of considered measures to correctly detect or estimate the quantum critical point and the non-trivial factorization point possessed by the spin chain., 29 pages, 8 figures. A review paper accepted for publication in the special issue Entanglement Entropy in the journal Entropy

We consider the dynamics of the quantum XY chain with disorder under the general assumption that the expectation of the eigenfunction correlator of the associated one-particle Hamiltonian satisfies a decay estimate typical of Anderson localization. We show that, starting from a broad class of product initial states, entanglement remains bounded for all times. For the XX chain, we also derive bounds on the particle transport which, in particular, show that the density profile of initial states that consist of fully occupied and empty intervals, only have significant dynamics near the edges of those intervals, uniformly for all times., Comment: 22 pages, final version, to appear in Lett. Math. Phys

We study entropic functionals/fluctuations of the XY chain with Hamiltonian $$\begin{array}{ll} \frac{1}{2} \sum\limits_{x \in \mathbb{Z}}J_x( \sigma_x^{(1)} \sigma_{x+1}^{(1)} +\sigma_x^{(2)} \sigma_{x+1}^{(2)}) + \lambda_x \sigma_x^{(3)}\end{array}$$ where initially the left (x ≤ 0)/right (x > 0) part of the chain is in thermal equilibrium at inverse temperature β l /β r . The temperature differential results in a non-trivial energy/entropy flux across the chain. The Evans–Searles (ES) entropic functional describes fluctuations of the flux observable with respect to the initial state while the Gallavotti–Cohen (GC) functional describes these fluctuations with respect to the steady state (NESS) the chain reaches in the large time limit. We also consider the full counting statistics (FCS) of the energy/entropy flux associated with a repeated measurement protocol, the variational entropic functional (VAR) that arises as the quantization of the variational characterization of the classical Evans–Searles functional and a natural class of entropic functionals that interpolate between FCS and VAR. We compute these functionals in closed form in terms of the scattering data of the Jacobi matrix hu x = J x u x+1 + λ x u x + J x−1 u x−1 canonically associated with the XY chain. We show that all these functionals are identical if and only if h is reflectionless (we call this phenomenon entropic identity). If h is not reflectionless, then the ES and GC functionals remain equal but differ from the FCS, VAR and interpolating functionals. Furthermore, in the non-reflectionless case, the ES/GC functional does not vanish at α = 1 (i.e., the Kawasaki identity fails) and does not have the celebrated α ↔ 1 − α symmetry. The FCS, VAR and interpolating functionals always have this symmetry. In the Schrodinger case, where J x = J for all x, the entropic identity leads to some unexpected open problems in the spectral theory of one-dimensional discrete Schrodinger operators.

We revisit the problem of finding the probability distribution of a fermionic number of one-dimensional spinless free fermions on a segment of a given length. The generating function for this probability distribution can be expressed as a determinant of a Toeplitz matrix. We use the recently proven generalized Fisher--Hartwig conjecture on the asymptotic behavior of such determinants to find the generating function for the full counting statistics of fermions on a line segment. Unlike the method of bosonization, the Fisher--Hartwig formula correctly takes into account the discreteness of charge. Furthermore, we check numerically the precision of the generalized Fisher--Hartwig formula, find that it has a higher precision than rigorously proven so far, and conjecture the form of the next-order correction to the existing formula., Comment: 17 pages, 2 figures, Latex, iopart.cls

The recent interest in aspects common to quantum information and condensed matter has prompted a prosperous activity at the border of these disciplines that were far distant until few years ago. Numerous interesting questions have been addressed so far. Here we review an important part of this field, the properties of the entanglement in many-body systems. We discuss the zero and finite temperature properties of entanglement in interacting spin, fermionic and bosonic model systems. Both bipartite and multipartite entanglement will be considered. At equilibrium we emphasize on how entanglement is connected to the phase diagram of the underlying model. The behavior of entanglement can be related, via certain witnesses, to thermodynamic quantities thus offering interesting possibilities for an experimental test. Out of equilibrium we discuss how to generate and manipulate entangled states by means of many-body Hamiltonians., Comment: 61 pages, 29 figures