New Canonical and Grand Canonical Density of States Techniques for Finite Density Lattice QCD

• Published in: Particles Vol. 3; no. 1; pp. 87 - 98
• Main Authors: Gattringer, Christof, Mandl, Michael, Törek, Pascal
• Format: Journal Article
• Language: English
• Published: MDPI AG 01-03-2020
• Subjects: density of states techniques; finite density; lattice qcd
• ISSN: 2571-712X; 2571-712X
• DOI: 10.3390/particles3010008

We discuss two new density of states approaches for finite density lattice QCD (Quantum Chromo Dynamics). The paper extends a recent presentation of the new techniques based on Wilson fermions, while here, we now discuss and test the case of finite density QCD with staggered fermions. The first of our two approaches is based on the canonical formulation where observables at a fixed net quark number N are obtained as Fourier moments of the vacuum expectation values at imaginary chemical potential θ . We treat the latter as densities that can be computed with the recently developed functional fit approach. The second method is based on a direct grand canonical evaluation after rewriting the QCD partition sum in terms of a suitable pseudo-fermion representation. In this form, the imaginary part of the pseudo-fermion action can be identified and the corresponding density may again be computed with the functional fit approach. We develop the details of the two approaches and discuss some exploratory first tests for the case of free fermions where reference results for assessing the new techniques may be obtained from Fourier transformation.