New approach to lattice QCD at finite density; results for the critical end point on coarse lattices

Abstract

All approaches currently used to study finite baryon density lattice QCD suffer from uncontrolled systematic uncertainties in addition to the well-known sign problem. We formulate and test an algorithm, sign reweighting, that works directly at finite $\mu ={\mu }_B/3$ and is yet free from any such uncontrolled systematics. With this algorithm the {\em only} problem is the sign problem itself. This approach involves the generation of configurations with the positive fermionic weight $|\mathrm{Re}\det D(\mu )|$ where $D(\mu )$ is the Dirac matrix and the signs $\mathrm{sign}(\mathrm{Re}\det D(\mu ))=\pm 1$ are handled by a discrete reweighting. Hence there are only two sectors, $+1$ and $-1$ and as long as the average $⟨\pm 1⟩\ne 0$ (with respect to the positive weight) this discrete reweighting by the signs carries no overlap problem and the results are reliable. The approach is tested on $N_t=4$ lattices with $2+1$ flavors and physical quark masses using the unimproved staggered discretization. By measuring the Fisher (sometimes also called Lee-Yang) zeros in the bare coupling on spatial lattices $L/a=8,10,12$ we conclude that the cross-over present at $\mu =0$ becomes stronger at $\mu >0$ and is consistent with a true phase transition at around ${\mu }_B/T\sim 2.4$.

13 pages, 17 figures, references added

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Cited by in corpus (3)

• Preparation of the SU(3) Lattice Yang-Mills Vacuum with Variational Quantum Methods
• Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density
• NNLO HTLpt predictions for the curvature of the QCD phase transition line