Abstract
Lattice spin-fermion models are important to study correlated systems where quantum dynamics allows for
a separation between slow and fast degrees of freedom. The fast degrees of freedom are treated quantum
mechanically while the slow variables, generically referred to as the “spins,” are treated classically. At present,
exact diagonalization coupled with classical Monte Carlo (ED+MC) is extensively used to solve numerically a
general class of lattice spin-fermion problems. In this common setup, the classical variables (spins) are treated
via the standard MC method while the fermion problem is solved by exact diagonalization. The “traveling cluster
approximation” (TCA) is a real space variant of the ED+MC method that allows to solve spin-fermion problems
on lattice sizes with up to 103 sites. In this publication, we present a novel reorganization of the TCA algorithm
in a manner that can be efficiently parallelized. This allows us to solve generic spin-fermion models easily on 104
lattice sites and with some effort on 105 lattice sites, representing the record lattice sizes studied for this family
of models.
