Antiferromagnetic correlations in almost-localized Fermi liquids

TLDR

In the almost‑localized limit, the system is best described by an effective Hamiltonian separating the kinetic energy of charge carriers from Heisenberg spin‑spin coupling. The authors employ a Monte Carlo approach to evaluate one‑band Gutzwiller wave functions, testing Gutzwiller’s kinetic‑energy approximation for both ground and excited states. The authors find that nearly half‑filled bands display strong antiferromagnetic short‑range correlations that disappear with uniform band occupation and exist only at temperatures below the coherence temperature, and that these correlations, induced by restricted charge fluctuations, allow the almost‑localized Fermi liquid to lower its energy through both kinetic and spin terms, stabilizing the ground state.

Abstract

A Monte Carlo method is used to calculate various properties of one-band Gutzwiller wave functions which are formed by restricting the charge fluctuations in noninteracting wave functions. Gutzwiller's approximate formula for the kinetic energy is tested both for the ground state and excited states. The ground state is found to have strong antiferromagnetic short-range spin-spin correlations for nearly-half-filled bands, thus extending previous work on the half-filled case. These correlations are very sensitive to the choice of occupied Bloch states and when the occupation is distributed uniformly over the band they disappear. From this fact we conclude that correlations are present only at temperatures low compared to the coherence temperature. In the almost-localized limit it is advantageous to describe the system by an effective Hamiltonian which separates into a term due to the kinetic energy of the charge carriers and one due to the Heisenberg spin-spin coupling. We show that the almost-localized Fermi liquid can gain energy from both terms in the effective Hamiltonian. In other words the restrictions on charge fluctuations can cause spin correlations which in turn can stabilize the Fermi-liquid ground state.