Generalized Hartree Fock Theory for Dispersion Relations of Interacting Fermionic Lattice Systems

TL;DR

This paper develops a variational approach using fermionic Gaussian states to analyze dispersion relations in interacting fermionic lattice systems, providing a new method to study low-lying excitations.

Contribution

It introduces a locally optimal 'gaussification' process and linearizes the equations to compute dispersion relations in fermionic lattice models.

Findings

Applied to 2D Hubbard model, capturing dispersion relations.

Provides a variational method for low-lying excited states.

Demonstrates the effectiveness of fermionic Gaussian states in complex systems.

Abstract

We study the variational solution of generic interacting fermionic lattice systems using fermionic Gaussian states and show that the process of "gaussification", leading to a nonlinear closed equation of motion for the covariance matrix, is locally optimal in time by relating it to the time-dependent variational principle. By linearising our nonlinear equation of motion around the ground-state fixed point we describe a method to study low-lying excited states leading to a variational method to determine the dispersion relations of generic interacting fermionic lattice systems. This procedure is applied to study the attractive and repulsive Hubbard model on a two-dimensional lattice.