skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model

Abstract

We analyze the finite-size scaling exponents in the Lipkin-Meshkov-Glick model by means of the Holstein-Primakoff representation of the spin operators and the continuous unitary transformations method. This combination allows us to exactly compute the leading corrections to the ground-state energy, the gap, the magnetization, and the two-spin correlation functions. We also present numerical calculations for large system size which confirm the validity of this approach. Finally, we use these results to discuss the entanglement properties of the ground state focusing on the (rescaled) concurrence that we compute in the thermodynamical limit.

Authors:
 [1];  [2]
  1. Institut fuer Theoretische Physik, Universitaet zu Koeln, Zuelpicher Strasse. 77, 50937 Cologne (Germany)
  2. Laboratoire de Physique Theorique de la Matiere Condensee, CNRS UMR 7600, Universite Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05 (France)
Publication Date:
OSTI Identifier:
20719054
Resource Type:
Journal Article
Journal Name:
Physical Review. B, Condensed Matter and Materials Physics
Additional Journal Information:
Journal Volume: 71; Journal Issue: 22; Other Information: DOI: 10.1103/PhysRevB.71.224420; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1098-0121
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 36 MATERIALS SCIENCE; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CORRECTIONS; CORRELATION FUNCTIONS; ENERGY GAP; FOCUSING; GROUND STATES; HAMILTONIANS; J-J COUPLING; MAGNETIZATION; QUANTUM ENTANGLEMENT; SPIN; TRANSFORMATIONS

Citation Formats

Dusuel, Sebastien, and Vidal, Julien. Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model. United States: N. p., 2005. Web. doi:10.1103/PhysRevB.71.224420.
Dusuel, Sebastien, & Vidal, Julien. Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model. United States. https://doi.org/10.1103/PhysRevB.71.224420
Dusuel, Sebastien, and Vidal, Julien. Wed . "Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model". United States. https://doi.org/10.1103/PhysRevB.71.224420.
@article{osti_20719054,
title = {Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model},
author = {Dusuel, Sebastien and Vidal, Julien},
abstractNote = {We analyze the finite-size scaling exponents in the Lipkin-Meshkov-Glick model by means of the Holstein-Primakoff representation of the spin operators and the continuous unitary transformations method. This combination allows us to exactly compute the leading corrections to the ground-state energy, the gap, the magnetization, and the two-spin correlation functions. We also present numerical calculations for large system size which confirm the validity of this approach. Finally, we use these results to discuss the entanglement properties of the ground state focusing on the (rescaled) concurrence that we compute in the thermodynamical limit.},
doi = {10.1103/PhysRevB.71.224420},
url = {https://www.osti.gov/biblio/20719054}, journal = {Physical Review. B, Condensed Matter and Materials Physics},
issn = {1098-0121},
number = 22,
volume = 71,
place = {United States},
year = {2005},
month = {6}
}