Momentum-Space Entanglement Spectrum of Bosons and Fermions with Interactions

Rex Lundgren, Jonathan Blair, Martin Greiter, Andreas Läuchli, Gregory A. Fiete, and Ronny Thomale
Phys. Rev. Lett. 113, 256404 – Published 18 December 2014
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Abstract

We study the momentum space entanglement spectra of bosonic and fermionic formulations of the spin-1/2 XXZ chain with analytical methods and exact diagonalization. We investigate the behavior of the entanglement gaps, present in both formulations, across quantum phase transitions in the XXZ chain. In both cases, finite size scaling suggests that the entanglement gap closure does not occur at the physical transition points. For bosons, we find that the entanglement gap observed in Thomale et al. [Phys. Rev. Lett. 105, 116805 (2010)] depends on the scaling dimension of the conformal field theory as varied by the XXZ anisotropy. For fermions, the infinite entanglement gap present at the XX point persists well past the phase transition at the Heisenberg point. We elaborate on how these shifted transition points in the entanglement spectra may support the numerical study of phase transitions in the momentum space density matrix renormalization group.

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  • Received 13 May 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.256404

© 2014 American Physical Society

Authors & Affiliations

Rex Lundgren1,*, Jonathan Blair1, Martin Greiter2, Andreas Läuchli3, Gregory A. Fiete1, and Ronny Thomale2

  • 1Department of Physics, The University of Texas at Austin, Austin, Texas 78712, USA
  • 2Insitute for Theoritical Physics, Univesity of Würzburg, D-97074 Würzburg, Germany
  • 3Institut für Theoretische Physik, Universität Innsbruck, Technikerstraße 25, A-6020 Innsbruck, Austria

  • *rexlund@physics.utexas.edu

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Issue

Vol. 113, Iss. 25 — 19 December 2014

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