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QCD in one dimension at nonzero chemical potential

L. Ravagli

J. J. M. Verbaarschot

  • Cyclotron Institute and Physics Department, TEXAS A&M University, College Station, Texas 77843-3366, USA

  • Niels Bohr International Academy, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark
  • Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen Ø, Denmark,
  • and Department of Physics and Astronomy, SUNY, Stony Brook, New York 11794, USA

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Phys. Rev. D 76, 054506 – Published 19 September, 2007

DOI: https://doi.org/10.1103/PhysRevD.76.054506

Abstract

Using an integration formula recently derived by Conrey, Farmer, and Zirnbauer, we calculate the expectation value of the phase factor of the fermion determinant for the staggered lattice QCD action in one dimension. We show that the chemical potential can be absorbed into the quark masses; the theory is in the same chiral symmetry class as QCD in three dimensions at zero chemical potential. In the limit of a large number of colors and fixed number of lattice points, chiral symmetry is broken spontaneously, and our results are in agreement with expressions based on a chiral Lagrangian. In this limit, the eigenvalues of the Dirac operator are correlated according to random matrix theory for QCD in three dimensions. The discontinuity of the chiral condensate is due to an alternative to the Banks-Casher formula recently discovered for QCD in four dimensions at nonzero chemical potential. The effect of temperature on the average phase factor is discussed in a schematic random matrix model.

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Phys. Rev. D 76, 054506– Published 19 September, 2007
  • Received 6 June 2007

© 2007 American Physical Society

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