Disorder by disorder and flat bands in the kagome transverse field Ising model

TL;DR

This paper investigates the quantum phase transitions and flat band phenomena in the kagome and triangular lattice transverse field Ising models, revealing a disorder by disorder scenario and extremely flat one-particle dispersions.

Contribution

It provides the first detailed analysis of disorder by disorder in the kagome transverse field Ising model and characterizes the flat band behavior through high-order series expansions.

Findings

Triangular lattice exhibits a second-order phase transition in the 3d XY class.

Kagome lattice shows a disorder by disorder scenario with finite gaps.

Kagome lattice has an extremely flat lowest one-particle dispersion from high-order effects.

Abstract

We study the transverse field Ising model on a kagome and a triangular lattice using high-order series expansions about the high-field limit. For the triangular lattice our results confirm a second-order quantum phase transition in the 3d XY universality class. Our findings for the kagome lattice indicate a notable instance of a disorder by disorder scenario in two dimensions. The latter follows from a combined analysis of the elementary gap in the high- and low-field limit which is shown to stay finite for all fields h. Furthermore, the lowest one-particle dispersion for the kagome lattice is extremely flat acquiring a dispersion only from order eight in the 1/h limit. This behaviour can be traced back to the existence of local modes and their breakdown which is understood intuitively via the linked cluster expansion.