Calculation of Entanglement Entropy in Fermion Lattices

POSTER

Abstract

We study bipartite entanglement entropies of the ground and excited states of model fermion systems, where a staggered potential, $\mu_s$, induces a gap in the spectrum. Ground state entanglement entropies satisfy the ``area law,'' and the ``area law coefficient'' is found to diverge as a logarithm of the staggered potential, when the system has an extended Fermi surface at $\mu_s=0$. On the square-lattice, we show that the coefficient of the logarithmic divergence depends on the Fermi surface geometry and its orientation with respect to the real-space interface between subsystems, and is related to the Widom conjecture as enunciated by Gioev and Klich (Phys. Rev. Lett. 96, 100503 (2006)). For point Fermi surfaces in two-dimension, the ``area-law'' coefficient stays finite as $\mu_s \rightarrow 0$. The von Neumann entanglement entropy associated with the excited states follows a ``volume law'' and allows us to calculate an entropy density function $s_V(e)$, which is substantially different from the thermodynamic entropy density function $s_T(e)$, when the lattice is bipartitioned into two equal subsystems but approaches the thermodynamic entropy density as the fraction of sites integrated out of the larger subsystem approaches unity.

Authors

  • Michelle Storms

    Ohio Wesleyan University

  • John Royston

    Ball State University, Naval Research Laboratory, Washington, DC 20375, USA, Univ of Cincinnati, KITP China, U.C. Berkeley, FNAL, Cornell, West Virginia University, University of Pittsburgh, The Ohio State University, Carnegie Mellon University, Miami University, University of Notre Dame, University of Nebraska-Lincoln, Miami Univ, Australia National Univ., Miami Univ., Univ. of Cincinnati, Physics and Astronomy Department, Ohio University, Athens, OH 45701, Australian National University, University of Toledo, The University of Toledo, University of Toledo, Wright Center for Photovoltaics Innovation and Commercialization, University of Cincinnati, University of California, Davis