Article

Valence Bond and von Neumann Entanglement Entropy in Heisenberg Ladders

Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada.
Physical Review Letters (Impact Factor: 7.73). 09/2009; 103(11):117203. DOI: 10.1103/PhysRevLett.103.117203
Source: PubMed

ABSTRACT We present a direct comparison of the recently proposed valence bond entanglement entropy and the von Neumann entanglement entropy on spin-1/2 Heisenberg systems using quantum Monte Carlo and density-matrix renormalization group simulations. For one-dimensional chains we show that the valence bond entropy can be either less or greater than the von Neumann entropy; hence, it cannot provide a bound on the latter. On ladder geometries, simulations with up to seven legs are sufficient to indicate that the von Neumann entropy in two dimensions obeys an area law, even though the valence bond entanglement entropy has a multiplicative logarithmic correction.

0 Bookmarks
 · 
165 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: The entanglement entropy of a noninteracting fermionic system confined to a two-dimensional honeycomb lattice on a torus is calculated. We find that the entanglement entropy can characterize Lifshitz phase transitions without a local order parameter. In the noncritical phase and critical phase with a nodal Fermi surface, the entanglement entropy satisfies an area law. The leading subarea term is a constant in the gapped phase rather than a logarithmic additive term in the gapless regime. The tuning of chemical potential allows for a nonzero Fermi surface, whose variation along a particular direction determines a logarithmic violation of the area law. We perform the scaling of entanglement entropy numerically and find agreement between the analytic and numerical results. Furthermore, we clearly show that an entanglement spectrum is equivalent to an edge spectrum.
    Journal of Physics A Mathematical and Theoretical 06/2014; 47(25):255301. DOI:10.1088/1751-8113/47/25/255301 · 1.77 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We present a method for improving measurements of the entanglement R\'enyi entropies in quantum Monte Carlo simulations by relating them with measurements of participation R\'enyi entropies. Exploiting the capability of building improved estimators for the latter allows to obtain very good estimates for entanglement R\'enyi entropies. When considering a full system instead of a bipartition, the method can be further ameliorated providing access to the thermodynamic R\'enyi entropies with high accuracy. We also explore a recently-proposed method for the reconstruction of the entanglement spectrum from entanglement R\'enyi entropies and finally show how potential entanglement Hamiltonians may be tested for their validity using a comparison with thermal R\'enyi entropies.
    Physical Review B 05/2014; 90(12). DOI:10.1103/PhysRevB.90.125105 · 3.66 Impact Factor
  • Source

Full-text (2 Sources)

Download
4 Downloads
Available from
Feb 2, 2015