Abstract
We investigate the properties of the half-filling point in lattice QCD (LQCD), in particular the disappearance of the sign problem and the emergence of an apparent particle-hole symmetry, and try to understand where these properties come from by studying the heavy-dense fermion determinant and the corresponding strong-coupling partition function (which can be integrated analytically). We then add in a first step an effective Polyakov loop gauge action (which reproduces the leading terms in the character expansion of the Wilson gauge action) to the heavy-dense partition function and try to analyze how some of the properties of the half-filling point change when leaving the strong coupling limit. In a second step, we take also the leading nearest-neighbor fermion hopping terms into account (including gauge interactions in the fundamental representation) and mention how the method could be improved further to incorporate the full set of nearest-neighbor fermion hoppings. Using our mean-field method, we also obtain an approximate (μ, T) phase diagram for heavy-dense LQCD at finite inverse gauge coupling β. Finally, we propose a simple criterion to identify the chemical potential beyond which lattice artifacts become dominant.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
P. de Forcrand, Simulating QCD at finite density, PoS(LAT2009)010 [arXiv:1005.0539] [INSPIRE].
D. Sexty, Progress in complex Langevin simulations of full QCD at non-zero density, Nucl. Phys. A 931 (2014) 856 [arXiv:1408.6767] [INSPIRE].
G. Aarts, F. Attanasio, B. Jäger, E. Seiler, D. Sexty and I.-O. Stamatescu, The phase diagram of heavy dense QCD with complex Langevin simulations, Acta Phys. Polon. Supp. 8 (2015) 405 [arXiv:1506.02547] [INSPIRE].
H.J. Rothe, Lattice gauge theories, World Sci. Lect. Notes Phys. 82, World Scientific, Singapore (2012) [ISBN:978-981-4365-86-4] [INSPIRE].
I. Montvay and G. Münster, Quantum fields on a lattice, Camb. Monogr. Math. Phys., Cambridge University Press, Cambridge U.K. (1994).
J. Langelage, M. Neuman and O. Philipsen, Heavy dense QCD and nuclear matter from an effective lattice theory, JHEP 09 (2014) 131 [arXiv:1403.4162] [INSPIRE].
R. De Pietri, A. Feo, E. Seiler and I.-O. Stamatescu, A model for QCD at high density and large quark mass, Phys. Rev. D 76 (2007) 114501 [arXiv:0705.3420] [INSPIRE].
K. Fukushima and Y. Hidaka, A model study of the sign problem in the mean-field approximation, Phys. Rev. D 75 (2007) 036002 [hep-ph/0610323] [INSPIRE].
J. Greensite and K. Splittorff, Mean field theory of effective spin models as a baryon fugacity expansion, Phys. Rev. D 86 (2012) 074501 [arXiv:1206.1159] [INSPIRE].
A. Dumitru, R.D. Pisarski and D. Zschiesche, Dense quarks and the fermion sign problem, in a SU(N) matrix model, Phys. Rev. D 72 (2005) 065008 [hep-ph/0505256] [INSPIRE].
M. Fromm, J. Langelage, S. Lottini, M. Neuman and O. Philipsen, Onset transition to cold nuclear matter from lattice QCD with heavy quarks, Phys. Rev. Lett. 110 (2013) 122001 [arXiv:1207.3005] [INSPIRE].
M. Fromm, J. Langelage, S. Lottini and O. Philipsen, The QCD deconfinement transition for heavy quarks and all baryon chemical potentials, JHEP 01 (2012) 042 [arXiv:1111.4953] [INSPIRE].
Open Access
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1509.00087
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Rindlisbacher, T., de Forcrand, P. Two-flavor lattice QCD with a finite density of heavy quarks: heavy-dense limit and “particle-hole” symmetry. J. High Energ. Phys. 2016, 51 (2016). https://doi.org/10.1007/JHEP02(2016)051
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP02(2016)051