Extend of the $\mathbb{Z}_2$-spin liquid phase on the Kagom\'e-lattice

TL;DR

This paper investigates the extent of the $ ext{Z}_2$-spin liquid phase on the Kagomé lattice by interpolating between an exactly solvable model and a low-energy Heisenberg model, revealing a phase transition characterized by symmetry breaking.

Contribution

It introduces a perturbative approach to study the topological phase's stability and maps out the phase boundary away from the Heisenberg point.

Findings

Identifies a phase transition out of the topological phase.

Characterizes the new phase by broken rotational symmetry.

Finds a unit cell involving six sites in the new phase.

Abstract

The $\mathbb{Z}_2$ topological phase in the quantum dimer model on the Kagom\'e-lattice is a candidate for the description of the low-energy physics of the anti-ferromagnetic Heisenberg model on the same lattice. We study the extend of the topological phase by interpolating between the exactly solvable parent Hamiltonian of the topological phase and an effective low-energy description of the Heisenberg model in terms of a quantum-dimer Hamiltonian. Therefore, we perform a perturbative treatment of the low-energy excitations in the topological phase including free and interacting quasi-particles. We find a phase transition out of the topological phase far from the Heisenberg point. The resulting phase is characterized by a spontaneously broken rotational symmetry and a unit cell involving six sites.