Ordering and Excitation in Orbital Compass Model on a Checkerboard Lattice

TL;DR

This paper investigates the orbital compass model on a checkerboard lattice, revealing how frustration and fluctuations influence orbital ordering and excitation dynamics through analytical and numerical methods.

Contribution

It introduces a detailed analysis of classical and quantum orbital compass models on a checkerboard lattice, highlighting the effects of frustration and fluctuation-induced order.

Findings

Degeneracy at the fully frustrated point is lifted by fluctuations.

Long-range staggered order of pseudo-spins emerges.

Identification of a tricritical point due to competing interactions.

Abstract

We study an orbital compass model on a checkerboard lattice where orbital degree of freedom is represented by the pseudo-spin operator. Competition arises from an Ising interaction for the $z$ component of pseudo-spins along the vertical/horizontal bonds and an Ising interaction for the $x$ component along diagonal bonds. Classical and quantum compass models are analyzed by utilizing several analytical methods and numerical simulations. At a fully frustrated point where the two Ising interactions compete with each other, a macroscopic number of orbital configurations are degenerate in a classical ground state. This degeneracy is lifted by thermal and quantum fluctuations, and a staggered long-range order of the $z$ component of the pseudo-spin is realized. A tricritical point for this order appears due to competition between the bond dependent Ising interactions. Roles of geometrical frustration on excitation dynamics are also examined.