Von Neumann and Renyi Entanglement Entropies in Spin Ladders

ORAL

Abstract

Density matrix renormalization group (DMRG) algorithm has proven a useful tool to calculate entanglement properties of one- and quasi-one-dimensional condensed matter systems, due to the fact that the reduced density matrix eigenvalue spectrum for some bipartitions of the system is avaliable as a by-product of the algorithm. In this talk, I will present calculations of the von Neumann and Renyi entanglement entropies (EE) on Heisenberg ladders up to seven legs using DMRG. For a bipartition into subregions A and B, the EE for even-leg ladders is constant for subregion sizes larger than the correlation length, while for odd-leg ladders has a logarithmic dependence on the subregion size. Our results indicate that in the limit of a large number of legs the von Neumann EE obeys an area law.

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Authors

  • Ivan Gonzalez

    • Centro de Supercomputacion de Galicia, Avda. de Vigo s/n, E-15705 Santiago de Compostela, Spain

  • Ann B. Kallin

    • Department of Physics and Astronomy, University of Waterloo, Ontario, N2L 3G1, Canada

  • Matthew B. Hastings

    • Microsoft Research, Station Q, CNSI Building, University of California, Santa Barbara, CA, 93106

  • Roger G. Melko

    • Department of Physics and Astronomy, University of Waterloo, Ontario, N2L 3G1, Canada