Direct simulations of small multi-fermion systems

TL;DR

This paper presents a method for simulating small multi-fermion lattice systems, specifically Hubbard models, using bit-based representations to efficiently handle fermion signs, with limitations due to exponential resource growth.

Contribution

It introduces a general simulation technique for fermionic systems that simplifies sign calculations and is tailored for small systems, with potential for future scaling improvements.

Findings

Effective bit-based fermion sign handling

Simulation of small Hubbard models demonstrated

Resource growth is exponential with system size

Abstract

I explore computer simulations of the dynamics of small multi-fermion lattice systems. The method is more general, but I concentrate on Hubbard type models where the fermions hop between a small number of connected sites. I use the natural mapping of fermion occupation numbers onto computer bits. Signs from fermion interchange are reduced to bit counting. The technique inherently requires computer resources growing exponentially with the system volume; so, it restricted to modestly small systems. Large volume results would require combining these techniques with further approximations, perhaps in a recursive renormalization group manner.