A Majorana Fermion t-J Model in One Dimension

TL;DR

This paper investigates a one-dimensional Majorana fermion model inspired by spin chains, using diagrammatic and numerical methods to explore its low-energy excitations and generalizations to multiple species.

Contribution

It introduces a rotation invariant Majorana t-J model in 1D, analyzing its properties and extending it to N species with SO(4) symmetry.

Findings

Insights into low-energy excitations of the model

Extension to N species with SO(4) symmetry

Potential implications for spin-1/2 chains

Abstract

We study a rotation invariant Majorana fermion model in one dimension using diagrammatic perturbation theory and numerical diagonalization of small systems. The model is inspired by a Majorana representation of the antiferromagnetic spin-1/2 chain, and it is similar in form to the t-J model of electrons, except that the Majorana fermions carry spin-1 and Z_2 charge. We discuss the implications of our results for the low-energy excitations of the spin-1/2 chain. We also discuss a generalization of our model from 3 species of Majorana fermions to N species; the SO(4) symmetric model is particularly interesting.