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 ${\mu }_B/T\sim 2.4$.

arXiv comment13 pages, 17 figures, references added

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• Lattice QCD equation of state at finite chemical potential from an alternative expansion scheme
• Preparation of the SU(3) Lattice Yang-Mills Vacuum with Variational Quantum Methods
• Quantum algorithms for transport coefficients in gauge theories
• Lattice simulations of the QCD chiral transition at real baryon density
• Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansion
• Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density
• Analytical structure of the equation of state at finite density: Resummation versus expansion in a low energy model
• Equation of state of a hot-and-dense quark gluon plasma: lattice simulations at real ${\mu }_B$ vs. extrapolations
• NNLO HTLpt predictions for the curvature of the QCD phase transition line
• New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential
• Exponential reduction of the sign problem at finite density in the 2+1D XY model via contour deformations
• From imaginary to real chemical potential QCD with functional methods
• Overview of the QCD phase diagram -- Recent progress from the lattice
• A Gaussian Process Generative Model for QCD Equation of State
• Corrections to the hadron resonance gas from lattice QCD and their effect on fluctuation-ratios at finite density
• Resummed lattice QCD equation of state at finite baryon density: strangeness neutrality and beyond