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Title: QCD sign problem for small chemical potential

Abstract

The expectation value of the complex phase factor of the fermion determinant is computed in the microscopic domain of QCD at nonzero chemical potential. We find that the average phase factor is nonvanishing below a critical value of the chemical potential equal to half the pion mass and vanishes exponentially in the volume for larger values of the chemical potential. This holds for QCD with dynamical quarks as well as for quenched and phase quenched QCD. The average phase factor has an essential singularity for zero chemical potential and cannot be obtained by analytic continuation from imaginary chemical potential or by means of a Taylor expansion. The leading order correction in the p-expansion of the chiral Lagrangian is calculated as well.

Authors:
 [1];  [1];  [2];  [3]
  1. Niels Bohr Institute, Blegdamsvej 17, DK-2100, Copenhagen O (Denmark)
  2. (Denmark)
  3. (United States)
Publication Date:
OSTI Identifier:
20929584
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 11; Other Information: DOI: 10.1103/PhysRevD.75.116003; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CHIRALITY; EXPECTATION VALUE; LAGRANGIAN FUNCTION; MASS; PIONS; POTENTIALS; POWER FACTOR; QUANTUM CHROMODYNAMICS; QUARKS; SINGULARITY

Citation Formats

Splittorff, K., Verbaarschot, J. J. M., Niels Bohr International Academy, Blegdamsvej 17, DK-2100, Copenhagen O, and Department of Physics and Astronomy, SUNY, Stony Brook, New York 11794. QCD sign problem for small chemical potential. United States: N. p., 2007. Web. doi:10.1103/PHYSREVD.75.116003.
Splittorff, K., Verbaarschot, J. J. M., Niels Bohr International Academy, Blegdamsvej 17, DK-2100, Copenhagen O, & Department of Physics and Astronomy, SUNY, Stony Brook, New York 11794. QCD sign problem for small chemical potential. United States. doi:10.1103/PHYSREVD.75.116003.
Splittorff, K., Verbaarschot, J. J. M., Niels Bohr International Academy, Blegdamsvej 17, DK-2100, Copenhagen O, and Department of Physics and Astronomy, SUNY, Stony Brook, New York 11794. Fri . "QCD sign problem for small chemical potential". United States. doi:10.1103/PHYSREVD.75.116003.
@article{osti_20929584,
title = {QCD sign problem for small chemical potential},
author = {Splittorff, K. and Verbaarschot, J. J. M. and Niels Bohr International Academy, Blegdamsvej 17, DK-2100, Copenhagen O and Department of Physics and Astronomy, SUNY, Stony Brook, New York 11794},
abstractNote = {The expectation value of the complex phase factor of the fermion determinant is computed in the microscopic domain of QCD at nonzero chemical potential. We find that the average phase factor is nonvanishing below a critical value of the chemical potential equal to half the pion mass and vanishes exponentially in the volume for larger values of the chemical potential. This holds for QCD with dynamical quarks as well as for quenched and phase quenched QCD. The average phase factor has an essential singularity for zero chemical potential and cannot be obtained by analytic continuation from imaginary chemical potential or by means of a Taylor expansion. The leading order correction in the p-expansion of the chiral Lagrangian is calculated as well.},
doi = {10.1103/PHYSREVD.75.116003},
journal = {Physical Review. D, Particles Fields},
number = 11,
volume = 75,
place = {United States},
year = {Fri Jun 01 00:00:00 EDT 2007},
month = {Fri Jun 01 00:00:00 EDT 2007}
}
  • We calculate an analogue of the average phase factor of the staggered fermion determinant at imaginary chemical potential. Our results from the lattice agree well with the analytical predictions in the microscopic regime for both quenched and phase-quenched QCD. We demonstrate that the average phase factor in the microscopic domain is dominated by the lowest-lying Dirac eigenvalues.
  • A nonperturbative study of field theories with a complex action, such as QCD at finite baryon density, is difficult due to the sign problem. We show that the relativistic Bose gas at finite chemical potential has a sign and 'silver blaze' problem, similar to QCD. We then apply stochastic quantization and complex Langevin dynamics to study this theory with nonperturbative lattice simulations. Independence of chemical potential at small and a transition to a condensed phase at large chemical potential are found. Lattices of size N{sup 4}, with N=4, 6, 8, 10, are used. We show that the sign problem ismore » severe, however, we find that it has no negative effect using this approach. This improves the prospects of applying stochastic quantization to QCD at nonzero density.« less
  • We determine the chiral phase transition line in (2+1)-flavor QCD for small values of the light quark chemical potential. We show that for small values of the chemical potential the curvature of the phase transition line can be deduced from an analysis of scaling properties of the chiral condensate and its susceptibilities. To do so we extend earlier studies of the magnetic equation of state in (2+1)-flavor QCD to finer lattice spacings, aT = 1/8. We use these universal scaling properties of the chiral order parameter to extract the curvature of the transition line at two values of the cutoff,more » aT = 1/4 and 1/8. We find that cutoff effects are small for the curvature parameter and determine the transition line in the chiral limit to leading order in the light quark chemical potential. We obtain T{sub c}({micro}{sub q})/T{sub c}(0)=1-0.059(2)(4)({micro}{sub q}/T){sup 2+}O({micro}{sub q}{sup 4}).« less
  • We determine the chiral phase transition line in (2+1)-flavor QCD for small values of the light quark chemical potential. We show that for small values of the chemical potential the curvature of the phase transition line can be deduced from an analysis of scaling properties of the chiral condensate and its susceptibilities. To do so we extend earlier studies of the magnetic equation of state in (2+1)-flavor QCD to finer lattice spacings, aT=1/8. We use these universal scaling properties of the chiral order parameter to extract the curvature of the transition line at two values of the cutoff, aT=1/4 andmore » 1/8. We find that cutoff effects are small for the curvature parameter and determine the transition line in the chiral limit to leading order in the light quark chemical potential. We obtain T{sub c}({mu}{sub q})/T{sub c}(0)=1-0.059(2)(4)({mu}{sub q}/T){sup 2}+O({mu}{sub q}{sup 4}).« less
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