Block spins and Chirality in Heisenberg model on Kagome and triangular lattices

TL;DR

This paper uses a block-spin renormalization method to analyze the Heisenberg model on Kagome and triangular lattices, revealing how chirality influences the effective models and their ground states.

Contribution

It introduces a block-spin approach that reduces the Heisenberg model to an effective model on a triangular lattice, highlighting the role of chirality in differentiating lattice behaviors.

Findings

Effective models constructed with block spins provide upper bounds on ground state energies.

Chiral-ordered variational states tend to have higher energies.

Chirality captures key differences between Kagome and triangular lattices.

Abstract

The Spin-1/2 Heisenberg Model (HM) is investigated using a block-spin renormalization approach on Kagome and triangular lattices. In both cases, after coarse graining the triangles on original lattice and truncation of the Hilbert space to the triangular ground state subspace, HM reduces to an effective model on a triangular lattice in terms of the triangular-block degrees of freedom i.e. the spin and the chirality quantum numbers. The chirality part of the effective Hamiltonian captures the essential difference between the two lattices. It is seen that simple eigenstates can be constructed for the effective model whose energies serve as upper bounds on the exact ground state energy of HM, and chiral-ordered variational states have high energies compared to the other variational states.