Spatial entanglement entropy in the ground state of the Lieb-Liniger model

C. M. Herdman, P.-N. Roy, R. G. Melko, and A. Del Maestro
Phys. Rev. B 94, 064524 – Published 31 August 2016

Abstract

We consider the entanglement between two spatial subregions in the Lieb-Liniger model of bosons in one spatial dimension interacting via a contact interaction. Using ground-state path integral quantum Monte Carlo we numerically compute the Rényi entropy of the reduced density matrix of the subsystem as a measure of entanglement. Our numerical algorithm is based on a replica method previously introduced by the authors, which we extend to efficiently study the entanglement of spatial subsystems of itinerant bosons. We confirm a logarithmic scaling of the Rényi entropy with subsystem size that is expected from conformal field theory, and compute the nonuniversal subleading constant for interaction strengths ranging over two orders of magnitude. In the strongly interacting limit, we find agreement with the known free fermion result.

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  • Received 20 June 2016

DOI:https://doi.org/10.1103/PhysRevB.94.064524

©2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsQuantum Information, Science & TechnologyAtomic, Molecular & OpticalStatistical Physics & ThermodynamicsParticles & Fields

Authors & Affiliations

C. M. Herdman1,2,3,*, P.-N. Roy3, R. G. Melko2,4, and A. Del Maestro5

  • 1Institute for Quantum Computing, University of Waterloo, Ontario, N2L 3G1, Canada
  • 2Department of Physics & Astronomy, University of Waterloo, Ontario, N2L 3G1, Canada
  • 3Department of Chemistry, University of Waterloo, Ontario, N2L 3G1, Canada
  • 4Perimeter Institute for Theoretical Physics, Waterloo, Ontario, N2L 2Y5, Canada
  • 5Department of Physics, University of Vermont, Burlington, Vermont 05405, USA

  • *cherdman@uwaterloo.ca

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Issue

Vol. 94, Iss. 6 — 1 August 2016

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