Entanglement in Many-Body Systems

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 figure

Ground state entanglement in quantum spin chains

A microscopic calculation of ground state entanglement for the XY and Heisenberg models shows the emergence of universal scaling behavior at quantum phase transitions. Entanglement is thus controlled by conformal symmetry. Away from the critical point, entanglement gets saturated by a mass scale. Results borrowed from conformal field theory imply irreversibility of entanglement loss along renormalization group trajectories. Entanglement does not saturate in higher dimensions which appears to limit the success of the density matrix renormalization group technique. A possible connection between majorization and renormalization group irreversibility emerges from our numerical analysis.Comment: 26 pages, 16 figures, added references, minor changes. Final versio

Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems

This article reviews recent developments in the theoretical understanding and the numerical implementation of variational renormalization group methods using matrix product states and projected entangled pair states.Comment: Review from 200

Ground-state separability and criticality in interacting many-particle systems

We analyze exact ground state (GS) separability in general N-particle systems with two-site couplings. General necessary and sufficient conditions for full separability in the form of one- and two-site eigenvalue equations are first derived. The formalism is then applied to a class of SU(n)-type interacting systems where each constituent has access to n-local levels, and where the total number parity of each level is preserved. Explicit factorization conditions for parity-breaking GSs are obtained, which generalize those for XYZ spin systems and correspond to a fundamental GS multilevel parity transition where the lowest 2n-1 energy levels cross. We also identify a multicritical factorization point with exceptional high degeneracy proportional to Nn-1, arising when the total occupation number of each level is preserved, in which any uniform product state is an exact GS. Critical entanglement properties (such as full range pairwise entanglement) are shown to emerge in the immediate vicinity of factorization. Illustrative examples are provided.Fil: Petrovich, Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Canosa, Norma Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; ArgentinaFil: Rossignoli, Raúl Dante. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentin

Dynamics of Entanglement in one and two-dimensional spin systems

We present a review of dynamics of entanglement in one and two dimensional systems under the effect of external magnetic field and different degrees of anisotropy at zero and finite temperatures. Different techniques for treating the spin systems with large Hilbert space dimensions are discussed such as trace minimization algorithm, time-evolution matrix transformation and step by step projection technique.Comment: review article to appear in: To appear in Adv. Chem. Phys. (2013