Strong Coupling Lattice QCD in the Continuous Time Limit

TL;DR

This paper introduces a continuous time limit approach for lattice QCD with staggered fermions, simplifying computations by eliminating the need for continuum extrapolation and reducing the sign problem, with results validated against traditional discrete lattice methods.

Contribution

The authors develop a continuous time formulation of lattice QCD with an efficient worm algorithm, removing the continuum extrapolation and sign problem issues present in traditional discrete lattice simulations.

Findings

No continuum extrapolation needed in the continuous time limit.

Faster Monte Carlo simulations with no sign problem.

Consistent results with discrete lattice computations at zero and finite temperature.

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.