Majorana Diagrammatics for Quantum Spin-1/2 Models

TL;DR

This paper introduces a Majorana diagrammatic formalism for quantum spin-1/2 models, enabling standard many-body techniques without projections, and demonstrates its effectiveness through perturbative corrections to the Heisenberg model.

Contribution

It develops a new diagrammatic approach for spin-1/2 systems using Majorana fermions, simplifying calculations and improving mean-field results.

Findings

Perturbative corrections significantly improve mean-field results.

The formalism is applicable to 1D and 2D Heisenberg models.

Numerical results show qualitative and quantitative improvements.

Abstract

A diagrammatic formalism for lattices of 1/2 is developed. It is based on an unconstrained mapping between spin and Majorana operators. This allows the use of standard tools of diagrammatic quantum many-body theory without requiring projections. We derive, in particular, the Feynman rules for the expansion around a color-preserving mean-field theory. We then present the numerical results obtained by computing the corrections up to second order for the Heisenberg model in one and two dimensions, showing that perturbative corrections are not only numerically important, but also qualitatively improve the results of mean-field theory. These results pave the way for the use of Majorana diagrammatic tools in theoretical and numerical studies of quantum spin systems.