Functional Integrals for Correlated Fermions

TL;DR

This paper introduces a spin-rotation invariant functional integral formalism for strongly correlated fermion systems, offering new insights into magnetic phenomena and spectral properties in models like the Hubbard model.

Contribution

It develops a novel formalism using a space- and time-dependent spin reference axis to address spin-rotation invariance issues in correlated fermion models.

Findings

Proposes an alternative to Nagaoka ferromagnetism near half-filling.

Discusses spectral properties in a short-range ordered antiferromagnet.

Provides a framework for systematic improvements of mean-field theories.

Abstract

Functional integral methods provide a way to define mean--field theories and to systematically improve them. For the Hubbard model and similar strong--correlation problems, methods based in particular on the Hubbard--Stratonovich transformation have however been plagued by difficulties to formulate the problem in a spin--rotation invariant way. Here a formalism circumventing this problem by using a space-- and time--dependent spin reference axis is discussed. This formulation is then used to suggest a possible alternative to Nagaoka ferromagnetism in the strongly correlated Hubbard model in the vicinity of half--filling. Finally, some aspects of single--particle spectra in a simplified model for a short--range ordered antiferromagnet are discussed.