Random phase approximation for the 1D anti-ferromagnetic Heisenberg model

TL;DR

This paper applies the Hartree-Fock-RPA method to the 1D anti-ferromagnetic Heisenberg model, showing reasonable spectral results and improvements with self-consistent RPA in finite chains.

Contribution

It introduces the application of Hartree-Fock-RPA and Self-Consistent RPA to the 1D Heisenberg model, providing new insights into spectral functions and sum rules.

Findings

Reasonable spectral function results in symmetry unbroken phase

Improved results with Self-Consistent RPA in finite chains

Validation of RPA approaches for 1D anti-ferromagnetic systems

Abstract

The Hartree-Fock-RPA approach is applied to the 1D anti-ferromagnetic Heisenberg model in the Jordan-Wigner representation. Somewhat contrary to expectation, this leads to reasonable results for spectral functions and sum rules in the symmetry unbroken phase. In a preliminary application of Self-Consistent RPA to finite size chains strongly improved results are obtained.