Valence Bond Solid Phases on Deformed Kagome Lattices: Application to Rb2Cu3SnF12

TL;DR

This paper investigates how small lattice distortions in the Kagome lattice, similar to those in Rb2Cu3SnF12, influence the quantum ground states, revealing a transition from a 36-site to a 12-site valence bond solid phase.

Contribution

The study introduces a detailed analysis of valence bond solid phases on deformed Kagome lattices, highlighting the sensitivity of the 36-site phase and proposing a more likely 12-site phase for Rb2Cu3SnF12.

Findings

The 36-site valence bond solid phase is highly sensitive to lattice distortions.

A 12-site valence bond solid phase with a pinwheel structure is more probable in Rb2Cu3SnF12.

Deformations significantly modify the excitation spectra of the system.

Abstract

Motivated by a recent experiment on Rb2Cu3SnF12, where spin-1/2 Cu2+ moments reside on the layers of Kagome-like lattices, we investigate quantum ground states of the antiferromagnetic Heisenberg model on a series of deformed Kagome lattices. The deformation is characterized by a weaker exchange coupling (alpha*J) on certain lattice links appropriate for Rb2Cu3SnF12 with alpha=1 corresponding to the ideal Kagome lattice. In particular, we study possible valence bond solid phases using the perturbation theory around isolated dimer limits, dimer series expansion, and self-consistent bond operator mean field theory. It is shown that the valence bond solid phase with a 36-site unit cell of the ideal Kagome lattice is quite sensitive to a small lattice distortion as the kind discovered in Rb2Cu3SnF12. As a result, we find that a more likely quantum ground state in Rb2Cu3SnF12 is the valence bond solid phase with a 12-site unit cell, where six dimers form a pinwheel structure, leading to strong modification of the elementary triplet and singlet excitation spectra in the deformed Kagome lattices.