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

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 ${\gamma }^2\simeq a\mathrm{/}\text{at}$ and the number of time-slices $N_{\tau }$ to infinity, keeping the ratio $\gamma^2/N_\tau \simeq aT$fixed\mathrm{.}Inthislimit,ambiguitiesarisingfromtheanisotropyparameter$\gamma$ are eliminated and discretization errors usually introduced by a finite temporal lattice extent $\text{Nt}$ are absent. The obvious gain is that no continuum extrapolation $N_{\tau }\to \mathrm{\infty }$ 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 $\text{Nt}$ in previous studies turn out to be large at low temperatures.