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 pexpansion of the chiral Lagrangian is calculated as well.
 Authors:
 Niels Bohr Institute, Blegdamsvej 17, DK2100, Copenhagen O (Denmark)
 (Denmark)
 (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, DK2100, 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, DK2100, 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, DK2100, 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, DK2100, 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 pexpansion 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 phasequenched QCD. We demonstrate that the average phase factor in the microscopic domain is dominated by the lowestlying Dirac eigenvalues.

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