The Hubbard model in the canonical formulation

TL;DR

This paper reformulates the Hubbard model using a canonical transfer matrix approach, simplifying the fermionic degrees of freedom and demonstrating the absence of the sign problem in 1+1 dimensions, with improved estimators for key physical quantities.

Contribution

It introduces a novel canonical formulation of the Hubbard model with transfer matrices, eliminating auxiliary fields and connecting to fermion loop and bag formulations.

Findings

Sign problem is absent in 1+1 dimensions.

Partition function factorizes in time.

Improved estimators for physical observables.

Abstract

We describe non-relativistic fermions on the lattice (Hubbard model) in the canonical formulation using transfer matrices in fixed fermion number sectors such that the partition function becomes fully factorized in time. By analytically integrating out the auxiliary Hubbard-Stratanovich field due to the four-fermion interaction, we express the system in terms of discrete, local fermion occupation numbers which are the only remaining degrees of freedom. We show the close relation to the fermion loop and the fermion bag formulation. One can prove that in 1+1 dimension the fermion sign problem is absent. Finally, we construct improved estimators for the ground state energy, 2-point functions, and for the chemical potential.