Correlated Cluster Algorithm: Quantum Monte Carlo for Lattice Gauge Theory

The Hamiltonian formulation of lattice gauge theories offers a pathway to new Monte Carlo algorithms and quantum protocols relevant to particle physics. Sampling configurations of gauge theories with Quantum Monte Carlo is difficult since Gauss’s law has to be obeyed and sign problems can occur.

In this talk, I will present the Correlated Cluster Algorithm, which can solve Gauss’s law and overcome the sign problem associated with a topological theta angle. Concretely, we add constraints to a Meron cluster algorithm to implement different types of Abelian gauge theories in (1+1)d, including quantum link models. The sign problem of the pure fermionic theory is completely removed by solving the constraints associated with Gauss’s law. The new algorithm provides a concrete example of the extension of cluster algorithms to cases where clusters are strongly correlated and can explore gauge theories beyond the limits of other numerical methods.