Diagrammatic approximations for the 2d quantum antiferromagnet: exact projection of auxiliary fermions

TL;DR

This paper develops diagrammatic approximations for the 2d quantum antiferromagnet's spin dynamics using auxiliary fermions, comparing two projection schemes and analyzing their temperature-dependent differences.

Contribution

It introduces a novel diagrammatic approach with exact projection for auxiliary fermions in the 2d Heisenberg antiferromagnet, extending beyond mean-field theory.

Findings

Differences between projection schemes increase at higher temperatures.

At zero temperature, both schemes yield identical results.

The method captures the correct dynamical scaling behavior.

Abstract

We present diagrammatic approximations to the spin dynamics of the 2d Heisenberg antiferromagnet for all temperatures, employing an auxiliary-fermion representation. The projection onto the physical subspace is effected by introducing an imaginary-valued chemical potential as proposed by Popov and Fedotov. The method requires that the fermion number at any lattice site is strictly conserved. We compare results obtained within a self-consistent approximation using two different auxiliary-particle projection schemes, (1) exact and (2) on average. Significant differences between the two are found at higher temperatures, whereas in the limit of zero temperature (approaching the magnetically ordered ground state) identical results emerge from (1) and (2), providing the qualitatively correct dynamical scaling behavior. An interpretation of these findings is given. We also present in some detail the derivation of the approximation, which goes far beyond mean-field theory and is formulated in terms of complex-valued spectral functions of auxiliary fermions.