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 obtained by sending both the anisotropy parameter $\xi=a_\sigma/a_\tau$ and the number of time-slices $N_\tau$ to infinity, keeping the ratio $aT=\xi/N\tau$ fixed. 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. We derive the continuous time partition function and the corresponding Hamiltonian formulation. We compare our computations with those on discrete lattices and study both zero and finite temperature properties of lattice QCD in this regime.
Highlights
The determination of the QCD phase diagram, in particular, the location of the critical end point (CEP), is an important, long-standing problem, requiring nonperturbative methods
In the strong coupling limit of lattice QCD (SC-LQCD) the sign problem is mild enough such that the full ðμB; TÞ phase diagram can be measured via Monte Carlo methods based on the dual variables
The continuous time worm algorithm (CT-WA) needs to fulfill detailed balance, such that the emission process is counterbalanced by an absorption process to obtain the equilibrium distribution of spatial dimers according to temperature and chemical potential
Summary
The determination of the QCD phase diagram, in particular, the location of the critical end point (CEP), is an important, long-standing problem, requiring nonperturbative methods. In lattice QCD, several approaches have been developed to investigate the phase transition from hadronic matter to the quark gluon plasma, but either they are limited to rather small μB=T, with μB the baryon chemical potential [1,2,3], or they cannot yet address full QCD [4,5,6] or study only low dimensional QCD-like toy models [7,8,9] The reason for this is the notorious sign problem [10], which arises because the fermion determinant for finite μB becomes complex, and importance sampling is no longer applicable. In the strong coupling limit of lattice QCD (SC-LQCD) the sign problem is mild enough such that the full ðμB; TÞ phase diagram can be measured via Monte Carlo methods based on the dual variables. In the Appendix, supplementary material for the various cross-checks of continuous time Monte Carlo and possible extensions such as for finite quark mass, more flavors, and isospin chemical potential are discussed
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