Flow equations for the one-dimensional Kondo lattice model: Static and dynamic ground state properties

TL;DR

This paper applies flow equations to analyze the one-dimensional Kondo lattice model, deriving an effective Hamiltonian and calculating static and dynamic properties, showing agreement with Luttinger liquid theory and RKKY interactions.

Contribution

It introduces a flow equation approach to derive an effective Hamiltonian for the 1D Kondo lattice and computes correlation functions using Schwinger boson mean field theory.

Findings

Static expectation values match Luttinger liquid behavior at small interactions

Estimated Luttinger parameter K_rho aligns with DMRG results

Effective Hamiltonian includes free electrons and RKKY-coupled spins

Abstract

The one-dimensional Kondo lattice model is investigated by means of Wegner's flow equation method. The renormalization procedure leads to an effective Hamiltonian which describes a free one-dimensional electron gas and a Heisenberg chain. The localised spins of the effective model are coupled by the well-known RKKY interaction. They are treated within a Schwinger boson mean field theory which permits the calculation of static and dynamic correlation functions. In the regime of small interaction strength static expectation values agree well with the expected Luttinger liquid behaviour. The parameter K_rho of the Luttinger liquid theory is estimated and compared to recent results from density matrix renormalization group studies.