Systematic Low-Energy Effective Field Theory for Magnons and Holes in an Antiferromagnet on the Honeycomb Lattice

TL;DR

This paper develops a systematic low-energy effective field theory for magnons and holes in doped antiferromagnets on the honeycomb lattice, revealing novel symmetry features and predicting an $f$-wave bound state.

Contribution

It introduces a new effective field theory framework for honeycomb lattice antiferromagnets, highlighting spontaneous symmetry breaking and bound state formation.

Findings

Doped holes are massive due to spontaneous symmetry breaking.

An accidental continuous spatial rotation symmetry emerges at leading order.

The ground state of two holes exhibits $f$-wave symmetry.

Abstract

Based on a symmetry analysis of the microscopic Hubbard and t-J models, a systematic low-energy effective field theory is constructed for hole-doped antiferromagnets on the honeycomb lattice. In the antiferromagnetic phase, doped holes are massive due to the spontaneous breakdown of the $SU(2)_s$ symmetry, just as nucleons in QCD pick up their mass from spontaneous chiral symmetry breaking. In the broken phase the effective action contains a single-derivative term, similar to the Shraiman-Siggia term in the square lattice case. Interestingly, an accidental continuous spatial rotation symmetry arises at leading order. As an application of the effective field theory we consider one-magnon exchange between two holes and the formation of two-hole bound states. As an unambiguous prediction of the effective theory, the wave function for the ground state of two holes bound by magnon exchange exhibits $f$-wave symmetry.