Perturbation Theory by Flow Equations: Dimerized and Frustrated S=1/2 Chain

TL;DR

This paper applies the flow equation method to derive effective Hamiltonians for dimerized and frustrated S=1/2 chains, providing detailed results on gaps, dispersion, and ground state energies.

Contribution

It demonstrates the use of flow equations as a perturbative tool for analyzing complex quantum spin chains, with explicit calculations for specific models.

Findings

Effective Hamiltonians conserve the number of excitations.

Clear separation of excitation sectors.

Quantitative results for gaps and energies.

Abstract

The flow equation method (Wegner 1994) is used as continuous unitary transformation to construct perturbatively effective Hamiltonians. The method is illustrated in detail for dimerized and frustrated antiferromagnetic S=1/2 chains. The effective Hamiltonians conserve the number of elementary excitations which are S=1 magnons for the dimerized chains. The sectors of different number of excitations are clearly separated. Easy-to-use results for the gap, the dispersion and the ground state energies of the chains are provided.