Functional Schr\"odinger Representations of Holstein-Primakoff Boson and Slave-Boson Theories for Heisenberg Antiferromagnets

TL;DR

This paper develops functional Schr"odinger representations for Holstein-Primakoff and slave-boson theories to analyze magnons in antiferromagnets, accurately predicting dispersion relations and exchange energies.

Contribution

It introduces a novel functional Schr"odinger framework for both Holstein-Primakoff and slave-boson theories applied to antiferromagnetic systems, linking two different approaches.

Findings

Accurate magnon dispersion relations in 2D antiferromagnets.

Correct prediction of exchange energy using Schr"odinger representation.

Equivalence of dispersion relations from slave-boson and Holstein-Primakoff approaches at half-filling.

Abstract

We present functional Schr\"odinger representations of Holstein-Primakoff boson and slave-boson theories for the Heisenberg Hamiltonian and the $t-J$ Hamiltonian respectively. Based on these representations we obtain the dispersion relations of magnons for two dimensional antiferromagnets. By applying the functional Schr\"odinger representation of the Holstein-Primakoff boson theory to the Heisenberg Hamiltonian, the exchange energy is correctly predicted and the self-energy of quasi-hole is obtained. From the use of the functional Schr\"odinger representation of the $t-J$ Hamiltonian it is shown that at half-filling the dispersion relation obtained from the slave-boson theory leads to that obtained from the Holstein-Primakoff boson approach.