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

References in corpus (2)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Pairing in fermionic systems: A quantum information perspective

Cited by in corpus (1)

• Ground States of Fermionic lattice Hamiltonians with Permutation Symmetry