Exploring Complex-Langevin Methods for Finite-Density QCD

QCD at non-zero chemical potential ($μ$) for quark number has a complex fermion determinant and thus standard simulation methods for lattice QCD cannot be applied. We therefore simulate this theory using the Complex-Langevin algorithm with Gauge Cooling in addition to adaptive methods, to prevent runaway behaviour. Simulations are performed at zero temperature on a $12^4$ lattice with 2 quarks which are light enough that $m_N/3$ is significantly larger than $m_π/2$. Preliminary results are qualitatively as expected. The quark-number density is close to zero for $μ< m_N/3$, beyond which it increases, eventually reaching its saturation value of $3$ for $μ$ sufficiently large. The chiral condensate decreases as $μ$ is increased approaching zero at saturation, while the plaquette increases towards its quenched value. We have yet to observe the transition to nuclear matter at $μ\approx m_N/3$, presumably because the runs for $μ$ between $m_N/3$ and saturation have yet to equilibrate.

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