• Open Access

Phase structure of the (1+1)-dimensional massive Thirring model from matrix product states

Mari Carmen Bañuls, Krzysztof Cichy, Ying-Jer Kao, C.-J. David Lin, Yu-Ping Lin, and David T.-L. Tan
Phys. Rev. D 100, 094504 – Published 20 November 2019

Abstract

Employing matrix product states as an ansatz, we study the nonthermal phase structure of the (1+1)-dimensional massive Thirring model in the sector of a vanishing total fermion number with staggered regularization. In this paper, details of the implementation for this project are described. To depict the phase diagram of the model, we examine the entanglement entropy, the fermion bilinear condensate, and two types of correlation functions. Our investigation shows the existence of two phases, with one of them being critical and the other gapped. An interesting feature of the phase structure is that the theory with the nonzero fermion mass can be conformal. We also find clear numerical evidence that these phases are separated by a transition of the Berezinskii-Kosterlitz-Thouless type. Results presented in this paper establish the possibility of using the matrix product states for probing this type of phase transition in quantum field theories. They can provide information for further exploration of scaling behavior, and they serve as an important ingredient for controlling the continuum extrapolation of the model.

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  • Received 28 August 2019

DOI:https://doi.org/10.1103/PhysRevD.100.094504

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Particles & Fields

Authors & Affiliations

Mari Carmen Bañuls*

  • Max-Planck Institut, für Quantenoptik, Garching 85748, Germany and Munich Center for Quantum Science and Technology (MCQST), Schellingstrasse 4, Munich 80799, Germany

Krzysztof Cichy

  • Faculty of Physics, Adam Mickiewicz University, Uniwersytetu Poznańskiego 2, 61-614 Poznań, Poland

Ying-Jer Kao

  • Department of Physics, National Taiwan University, Taipei 10617, Taiwan

C.-J. David Lin§

  • Institute of Physics, National Chiao-Tung University, Hsinchu 30010, Taiwan and Centre for High Energy Physics, Chung-Yuan Christian University, Chung-Li 32023, Taiwan

Yu-Ping Lin

  • Department of Physics, University of Colorado, Boulder, Colorado 80309, USA

David T.-L. Tan

  • Institute of Physics, National Chiao-Tung University, Hsinchu 30010, Taiwan

  • *banulsm@mpq.mpg.de
  • kcichy@amu.edu.pl
  • yjkao@phys.ntu.edu.tw
  • §dlin@mail.nctu.edu.tw
  • Yuping.Lin@colorado.edu
  • tanlin2013.py04g@nctu.edu.tw

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Issue

Vol. 100, Iss. 9 — 1 November 2019

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