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  • Letter
  • Open Access

Detecting the critical point through entanglement in the Schwinger model

Kazuki Ikeda1,2,*, Dmitri E. Kharzeev1,2,3,†, René Meyer4,5,‡, and Shuzhe Shi6,2,§

  • 1Co-design Center for Quantum Advantage, Stony Brook University, Stony Brook, New York 11794-3800, USA
  • 2Center for Nuclear Theory, Department of Physics and Astronomy, Stony Brook University, Stony Brook, New York 11794-3800, USA
  • 3Department of Physics, Brookhaven National Laboratory, Upton, New York 11973-5000, USA
  • 4Institute for Theoretical Physics and Astrophysics, Julius-Maximilians-Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
  • 5Würzburg-Dresden Cluster of Excellence (ct.qmat)
  • 6Department of Physics, Tsinghua University, Beijing 100084, China

  • *kazuki.ikeda@stonybrook.edu
  • †dmitri.kharzeev@stonybrook.edu
  • ‡rene.meyer@uni-wuerzburg.de
  • §shuzhe-shi@tsinghua.edu.cn
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Phys. Rev. D 108, L091501 – Published 9 November, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L091501

Abstract

Using quantum simulations on classical hardware, we study the phase diagram of the massive Schwinger model with a θ term at finite chemical potential μ. We find that the quantum critical point in the phase diagram of the model can be detected through the entanglement entropy and entanglement spectrum. As a first step, we chart the phase diagram using conventional methods by computing the dependence of the charge and chiral condensates on the fermion mass m, coupling constant g, and the chemical potential μ. At zero density, the Schwinger model possesses a quantum critical point at θ=π and m/g≃0.33. We find that the position of this quantum critical point depends on the chemical potential. Near this quantum critical point, we observe a sharp maximum in the entanglement entropy. Moreover, we find that the quantum critical point can be located from the entanglement spectrum by detecting the position of the gap closing point.

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Phys. Rev. D 108, L091501– Published 9 November, 2023
  • Received 18 May 2023
  • Accepted 13 October 2023
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