Effective Hamiltonians for holes in antiferromagnets: a new approach to implement forbidden double occupancy

TL;DR

This paper introduces a new coherent state approach to derive effective Hamiltonians for holes in antiferromagnets, rigorously implementing the forbidden double occupancy constraint and applying it to both collinear and non-collinear systems.

Contribution

The authors develop a novel coherent state framework that accurately incorporates the double occupancy constraint in effective Hamiltonians for holes in antiferromagnets.

Findings

Reproduces the known fermion-boson Hamiltonian for collinear antiferromagnets.

Successfully applies to non-collinear antiferromagnets, such as the triangular lattice.

Matches numerical results for the hole spectrum in the triangular antiferromagnet.

Abstract

A coherent state representation for the electrons of ordered antiferromagnets is used to derive effective Hamiltonians for the dynamics of holes in such systems. By an appropriate choice of these states, the constraint of forbidden double occupancy can be implemented rigorously. Using these coherent states, one arrives at a path integral representation of the partition function of the systems, from which the effective Hamiltonians can be read off. We apply this method to the t-J model on the square lattice and on the triangular lattice. In the former case, we reproduce the well-known fermion-boson Hamiltonian for a hole in a collinear antiferromagnet. We demonstrate that our method also works for non-collinear antiferromagnets by calculating the spectrum of a hole in the triangular antiferromagnet in the self-consistent Born approximation and by comparing it with numerically exact results.