Treating Fermions

Michael J. Creutz

I explore a recursive enumeration of world-line diagrams as a numerical approach to simulating many-fermion lattice systems. Signs from fermion exchange are treated exactly. In addition, all values of the coupling constants are treated simultaneously. The method is computationally fast, although large-memory requirements restrict it to small spatial systems.

Alex Kamenev

M. Laine, Aleksi Vuorinen

Jianzhou Zhao, Carlos A. Jiménez-Hoyos, Gustavo E. Scuseria +4 more

We present a mapping of elementary fermion operators onto a quadratic form of composite fermionic and bosonic cluster operators. The mapping is an exact isomorphism as long as the physical constraint of one composite particle per cluster is satisfied. This condition is treated on average in a composite particle mean-field approach, which consists of an ansatz that decouples the composite fermionic and bosonic sectors. The theory is tested on the 1D and 2D Hubbard models. Using a Bogoliubov determinant for the composite fermions and either a coherent or Bogoliubov state for the bosons, we obtain a simple and accurate procedure for treating the Mott insulating phase of the Hubbard model with mean-field computational cost.

Anamitra Mukherjee, Niravkumar D. Patel, Chris Bishop +1 more

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 10(3) 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 10(4) lattice sites and with some effort on 10(5) lattice sites, representing the record lattice sizes studied for this family of models.

C. J. Pethick, H. Smith