Complex Langevin Simulations of QCD at Finite Density – Progress Report

D K Sinclair,J B Kogut

doi:10.1051/epjconf/201817507031

D K Sinclair, J B Kogut

Open Access

https://doi.org/10.1051/epjconf/201817507031

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Abstract

We simulate lattice QCD at finite quark-number chemical potential to study nuclear matter, using the complex Langevin equation (CLE). The CLE is used because the fermion determinant is complex so that standard methods relying on importance sampling fail. Adaptive methods and gauge-cooling are used to prevent runaway solutions. Even then, the CLE is not guaranteed to give correct results. We are therefore performing extensive testing to determine under what, if any, conditions we can achieve reliable results. Our earlier simulations at β = 6/g2 = 5.6, m = 0.025 on a 124 lattice reproduced the expected phase structure but failed in the details. Our current simulations at β = 5.7 on a 164 lattice fail in similar ways while showing some improvement. We are therefore moving to even weaker couplings to see if the CLE might produce the correct results in the continuum (weak-coupling) limit, or, if it still fails, whether it might reproduce the results of the phase-quenched theory. We also discuss action (and other dynamics) modifications which might improve the performance of the CLE.

Highlights

We study the physics of nuclear matter, the constituent of neutron stars and the interiors of heavy nuclei
In lattice QCD at weak coupling, potential runaway solutions are controlled by adaptively readjusting the updating ‘time’ increment and implementing gauge cooling – choosing a gauge which minimizes the average unitarity norm, which is a measure of the distance of the gauge fields from the S U(3) manifold [12]
It has been suggested that keeping unitarity norms small increases the chance that the complex Langevin equation (CLE) will converge to the correct results, since there is less chance that the trajectories will encounter zeros of the fermion determinant. this suggests one should try even weaker couplings

Summary

Introduction

We study the physics of nuclear matter, the constituent of neutron stars and the interiors of heavy nuclei. Complex Langevin (CLE) simulations cannot be guaranteed to work unless the trajectories are restricted to a finite domain and the drift (force) term is holomorphic in the fields. Detailed discussion of these requirements as they pertain to QCD at finite μ are described in [5,6,7,8,9,10,11]. Preliminary indications from our simulations are that this is not true for lattice QCD at finite μ for these couplings It is still an open question as to whether the CLE produces the correct results, the phase-quenched results or neither in the weak-coupling limit. It is emphasized that gauge-cooling is essential for obtaining the correct results

Complex Langevin Equation for finite density Lattice QCD

Summary and Discussion