On the phase of quark determinant in lattice QCD with finite chemical potential

Abstract

We investigate the phase of the quark determinant with finite chemical potential in lattice QCD using both analytic and numerical methods. Applying the winding number expansion and the hopping parameter expansion to the logarithm of the determinant, we show that the absolute value of the phase has an upper bound that grows with the spatial volume but decreases exponentially with an increase in the temporal extent of the lattice. This analytic but approximate result is confirmed with a numerical study in four-flavor QCD in which the phase is calculated exactly. Since the phase is well controlled on lattices with larger time extents, we try the phase reweighting method in a region beyond $\mu /T=1$ where the Taylor expansion method cannot be applied. Working in four-flavor QCD, we find a first-order like behavior on a $6^3\times 4$ lattice at $\mu /T\approx 0.8$ which was previously observed by Kentucky group with the canonical method. We also show that the winding number expansion has a nice convergence property beyond $\mu /T=1$. We expect that this expansion is useful to study the high density region of the QCD phase diagram at low temperatures.

21 pages

References in corpus (7)

• Phase of the Fermion Determinant at Nonzero Chemical Potential
• The QCD Sign Problem for Small Chemical Potential
• Lee-Yang zero analysis for the study of QCD phase structure
• Finite density phase transition of QCD with $N_f=4$ and $N_f=2$ using canonical ensemble method
• A Random Matrix Study of the QCD Sign Problem
• The Approach to the Thermodynamic Limit in Lattice QCD at μ\neq0
• Winding expansion techniques for lattice QCD with chemical potential

Cited by in corpus (11)

• NANOGrav Signal from First-Order Confinement/Deconfinement Phase Transition in Different QCD Matters
• Interface Tension and Interface Entropy in 2+1 Flavour Nambu-Jona-Lasino Model
• NANOGrav hints for first-order confinement-deconfinement phase transition in different QCD-matter scenarios
• The cosmic QCD phase transition with dense matter and its gravitational waves from holography
• Complex Langevin calculations in QCD at finite density
• Finite size scaling study of $N_{\text{f}}=4$ finite density QCD on the lattice
• Curvature of the critical line on the plane of quark chemical potential and pseudo scalar meson mass for three-flavor QCD
• Towards extremely dense matter on the lattice
• Phase structure of $N_{\mathrm{f}}=3$ QCD at finite temperature and density by Wilson-Clover fermions
• Critical end point of Nf=3 QCD at finite temperature and density
• Finite size scaling for 4-flavor QCD with finite chemical potential