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Chiral condensate in the Schwinger model with matrix product operators

Mari Carmen Bañuls1,*, Krzysztof Cichy2,3,†, Karl Jansen4,‡, and Hana Saito5,§

  • 1Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Straße 1, 85748 Garching, Germany
  • 2Goethe-Universität Frankfurt am Main, Institut für Theoretische Physik, Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany
  • 3Adam Mickiewicz University, Faculty of Physics, Umultowska 85, 61-614 Poznan, Poland
  • 4NIC, DESY Zeuthen, Platanenallee 6, 15738 Zeuthen, Germany
  • 5Center for Computational Sciences, University of Tsukuba, Ibaraki 305-8577, Japan

  • *banulsm@mpq.mpg.de
  • †kcichy@th.physik.uni-frankfurt.de
  • ‡Karl.Jansen@desy.de
  • §saitouh@ccs.tsukuba.ac.jp
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Phys. Rev. D 93, 094512 – Published 24 May, 2016

DOI: https://doi.org/10.1103/PhysRevD.93.094512

Abstract

Tensor network (TN) methods, in particular the matrix product states (MPS) ansatz, have proven to be a useful tool in analyzing the properties of lattice gauge theories. They allow for a very good precision, much better than standard Monte Carlo (MC) techniques for the models that have been studied so far, due to the possibility of reaching much smaller lattice spacings. The real reason for the interest in the TN approach, however, is its ability, shown so far in several condensed matter models, to deal with theories which exhibit the notorious sign problem in MC simulations. This makes it prospective for dealing with the nonzero chemical potential in QCD and other lattice gauge theories, as well as with real-time simulations. In this paper, using matrix product operators, we extend our analysis of the Schwinger model at zero temperature to show the feasibility of this approach also at finite temperature. This is an important step on the way to deal with the sign problem of QCD. We analyze in detail the chiral symmetry breaking in the massless and massive cases and show that the method works very well and gives good control over a broad range of temperatures, essentially from zero to infinite temperature.

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Thermal evolution of the Schwinger model with matrix product operators

M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen, and H. Saito
Phys. Rev. D 92, 034519 (2015)

Article Text

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Phys. Rev. D 93, 094512– Published 24 May, 2016
  • Received 29 March 2016

© 2016 American Physical Society

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