Kagom{\'e} Lattice Antiferromagnet Stripped to Its Basics

TL;DR

This paper investigates a simplified one-dimensional model of a kagome lattice antiferromagnet, revealing that its low-energy excitations can be described by two critical Ising models with distinct velocities, highlighting localized Majorana fermions.

Contribution

It introduces a novel one-dimensional model capturing key features of the kagome lattice antiferromagnet and analyzes its low-energy spectrum using three different methods.

Findings

Low-energy spectrum described by two critical Ising models with different velocities

Presence of a strongly localized Majorana fermion due to small velocity

Triplet sector exhibits a spectral gap

Abstract

We study a model of a spin S = 1/2 Heisenberg antiferromagnet on a one dimensional lattice with the local symmetry of the two dimensional kagom{\'e} lattice. Using three complementary approaches, it is shown that the low energy spectrum can be described by two critical Ising models with different velocities. One of these velocities is small, leading to a strongly localized Majorana fermion. These excitations are singlet ones whereas the triplet sector has a spectral gap.