Continuous Time Monte Carlo for Lattice QCD in the Strong Coupling Limit

TL;DR

This paper introduces a continuous time Monte Carlo method for lattice QCD in the strong coupling limit, eliminating discretization errors and the sign problem, enabling efficient phase diagram computations without continuum extrapolation.

Contribution

The paper develops a continuous Euclidean time Monte Carlo algorithm for lattice QCD at infinite gauge coupling, removing discretization errors and simplifying phase diagram analysis.

Findings

Discretization errors at low temperatures are significantly reduced.

The algorithm is faster and free of the sign problem.

Phase diagram computed as a function of temperature and chemical potential.

Abstract

We present results for lattice QCD with staggered fermions in the limit of infinite gauge coupling, obtained from a worm-type Monte Carlo algorithm on a discrete spatial lattice but with continuous Euclidean time. This is achieved by sending both the anisotropy parameter $\gamma^2\simeq a/\at$ and the number of time-slices $N_\tau$ to infinity, keeping the ratio $\gamma^2/N_\tau \simeq aT$ fixed. In this limit, ambiguities arising from the anisotropy parameter $\gamma$ are eliminated and discretization errors usually introduced by a finite temporal lattice extent $\Nt$ are absent. The obvious gain is that no continuum extrapolation $N_\tau \rightarrow \infty$ has to be carried out. Moreover, the algorithm is faster and the sign problem disappears completely. As a first application, we determine the phase diagram as a function of temperature and real and imaginary baryon chemical potential. We compare our computations with those on lattices with discrete Euclidean time. Discretization errors due to finite $\Nt$ in previous studies turn out to be large at low temperatures.