# Finite Size Corrections to Entanglement in Quantum Critical Systems

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Marcelo S. Sarandy, Nov 16, 2013 Available from:- [Show abstract] [Hide abstract]

**ABSTRACT:**We study the Renyi entanglement entropy of an interval in a periodic spin chain, for a general eigenstate of a free, translational invariant Hamiltonian. In order to compute analytically the entropy we use two technical tools. The first one is used to reduce logarithmically the complexity of the problem and the second one to compute the R\'enyi entropy of the chosen subsystem. We introduce new strategies to perform the computations and derive new expressions for the entropy of these general states. Finally we show the perfect agreement of the analytical computations and the numerical results.Journal of Physics A Mathematical and Theoretical 01/2014; 47(24). DOI:10.1088/1751-8113/47/24/245301 · 1.69 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We study the entanglement entropy of a block of contiguous spins in excited states of spin chains. We consider the XY model in a transverse field and the XXZ Heisenberg spin-chain. For the latter, we developed a numerical application of algebraic Bethe Ansatz. We find two main classes of states with logarithmic and extensive behavior in the dimension of the block, characterized by the properties of excitations of the state. This behavior can be related to the locality properties of the Hamiltonian having a given state as ground state. We also provide several details of the finite size scaling.Journal of Statistical Mechanics Theory and Experiment 09/2009; 10(10). DOI:10.1088/1742-5468/2009/10/P10020 · 2.06 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The characterization of an infinite-order quantum phase transition (QPT) by entanglement measures is analyzed. To this aim, we consider two closely related solvable spin-1/2 chains, namely, the Ashkin-Teller and the staggered XXZ models. These systems display a distinct pattern of eigenstates but exhibit the same thermodynamics, i.e. the same energy spectrum. By performing exact diagonalization, we investigate the behavior of pairwise and block entanglement in the ground state of both models. In contrast with the XXZ chain, we show that pairwise entanglement fails in the characterization of the infinite-order QPT in the Ashkin-Teller model, although it can be achieved by analyzing the distance of the pair state from the separability boundary. Concerning block entanglement, we show that both XXZ and Ashkin-Teller models exhibit identical von Neumann entropies as long as a suitable choice of blocks is performed. Entanglement entropy is then shown to be able to identify the quantum phase diagram, even though its local extremes (either maximum or minimum) may also appear in the absence of any infinite-order QPT.Physical Review A 03/2010; 81:032334. DOI:10.1103/PhysRevA.81.032334 · 2.99 Impact Factor