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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 $γ^2\simeq a/\at$ and the number of time-slices $N_τ$ to infinity, keeping the ratio $γ^2/N_τ\simeq aT$ fixed. In this limit, ambiguities arising from the anisotropy parameter $γ$ are eliminated and discretization errors usually introduced by a finite temporal lattice extent $\Nt$ are absent. The obvious gain is that no continuum extrapolation $N_τ\rightarrow \infty$ 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.