New approach to lattice QCD at finite density; results for the critical end point on coarse lattices
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Springer
Received: April 29, 2020 Accepted: April 30, 2020 Published: May 19, 2020
Matteo Giordano, Kornel Kapas, Sandor D. Katz, Daniel Nogradi and Attila Pasztor Department of Theoretical Physics, ELTE Eotvos Lorand University, Pazmany Peter setany 1/a, Budapest 1117, Hungary
E-mail: [email protected], [email protected], [email protected], [email protected], [email protected] 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 = µB /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 h±1i 6= 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 Nt = 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 µB /T ∼ 2.4. Keywords: Lattice Quantum Field Theory, Phase Diagram of QCD ArXiv ePrint: 2004.10800
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP05(2020)088
JHEP05(2020)088
New approach to lattice QCD at finite density; results for the critical end point on coarse lattices
Contents 1
2 Path integral at finite µ
3
3 Numerical results 3.1 Monte-Carlo with µ > 0 3.2 Fisher zeros
4 5 6
4 Conclusion and outlook
1
10
Introduction
The numerical simulation of lattice QCD at finite baryon chemical potential is known to be hindered by the notorious sign problem: the fermionic determinant is not real and hence importance sampling techniques do not apply. Ways around the problem were nonetheless devised. These include Taylor expansion [1–14] around µ = µB /3 = 0, simulating at imaginary chemical potential [15–30], complex Langevin approach [31–37] and reweighting [38–43] from µ = 0.1 All of these approaches share the feature that for infinitesimally small µ at fixed spatial volume they are all expected to give correct results. Once µ is not infinitesimally small all approaches suffer from uncontrolled systematic uncertainties which render them unreliable. More precisely, the Taylor expansion method for non-infinitesimal µ requires the computation of high order µ-derivatives at µ = 0. It has the advantage that it provides well-defined physical quantities, namely the cumulants of the baryon numbe
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