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 µ = µ B /3 and is yet free from any such uncontrolled systematics. With this algorithm the only problem is the sign problem itself. This approach involves the generation of configurations with the positive fermionic weight |Re det D(µ)| where D(µ) is the Dirac matrix and the signs sign(Re det D(µ)) = ±1 are handled by a discrete reweighting. Hence there are only two sectors, +1 and −1 and as long as the average ±1 = 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 µ = 0 becomes stronger at µ > 0 and is consistent with a true phase transition at around µ B /T ∼ 2.4.

Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density

“…Application of these new methods using the stout-smeared action on coarse N τ " 4 lattices appears to signal a Lee-Yang zero at µ B " 2.4T [101], which however is is still far from the continuum. Simulation results on N τ " 6 for the renormalised chiral condensate,…”

“…It has then been proposed to redefine the rooted staggered determinant by a geometric matching procedure averaging over the quartets, after which it can be represented as an ordinary polynomial [99]. A further development [101] concerns the reweighting procedure, which usually is based on sampling with the phase quenched determinant and reweighting in the phase factor. This has a well-known overlap problem between the sampled and reweighted ensembles.…”

Finite chemical potential equation of state for QCD from an alternative expansion scheme

“…At finite baryon density lattice QCD faces a sign problem, due to the introduction of a real chemical potential that makes the action complex. Although new techniques that allow to directly simulate the theory at finite chemical potential exist [3,4], they cannot be applied to large scale QCD simulations yet.…”

Quantum algorithms for transport coefficients in gauge theories

“…Despite these issues, efforts have been undertaken to extract nonperturbative inputs [29] -e.g. parton distrubtion functions (PDFs) [33][34][35][36][37][38], phase diagrams [39][40][41][42], transport coefficients [43][44][45][46][47][48] -for the models from lattice QCD, albeit with large uncertainties.…”