An Improved Upper Bound for the Ground State Energy of Fermion Lattice Models

TL;DR

This paper introduces an improved method for estimating the ground state energy of fermion lattice models with sign problems, using deformed Hamiltonians and numerical simulations, especially effective in one-dimensional cases.

Contribution

It proposes a novel approach to bound ground state energies in fermion lattice models by employing sign-problem-free deformed Hamiltonians and numerical extrapolation techniques.

Findings

Effective bounds for 1D models demonstrated

Accurate estimation of ground state energies and correlations

Applicable to models like spinless fermions and Hubbard

Abstract

We present an improved upper bound for the ground state energy of lattice fermion models with sign problem. The bound can be computed by numerical simulation of a recently proposed family of deformed Hamiltonians with no sign problem. For one dimensional models, we expect the bound to be particularly effective and practical extrapolation procedures are discussed. In particular, in a model of spinless interacting fermions and in the Hubbard model at various filling and Coulomb repulsion we show how such techniques can estimate ground state energies and correlation function with great accuracy.