Ground-state phase structure of the spin-$\frac{1}{2}$ anisotropic planar pyrochlore

TL;DR

This paper investigates the ground-state phase diagram of a spin-1/2 anisotropic planar pyrochlore model using high-order coupled cluster method calculations, revealing various magnetic and valence-bond crystalline phases across different frustration levels.

Contribution

It provides the first comprehensive phase diagram of the anisotropic planar pyrochlore with arbitrary exchange signs using advanced coupled cluster calculations.

Findings

Identified multiple magnetic phases depending on frustration and exchange signs.

Calculated ground-state energy and local magnetization for various classical states.

Analyzed susceptibility to valence-bond crystalline ordering.

Abstract

We study the zero-temperature ground-state (GS) properties of the spin-$\frac{1}{2}$ anisotropic planar pyrochlore, using the coupled cluster method (CCM) implemented to high orders of approximation. The system comprises a $J_{1}$--$J_{2}$ model on the checkerboard lattice, with isotropic Heisenberg interactions of strength $J_{1}$ between all nearest-neighbour pairs of spins on the square lattice, and of strength $J_{2}$ between half of the next-nearest-neighbour pairs (in the checkerboard pattern). We calculate results for the GS energy and average local GS on-site magnetization, using various antiferromagnetic classical ground states as CCM model states. We also give results for the susceptibility of one of these states against the formation of crossed-dimer valence-bond crystalline (CDVBC) ordering. The complete GS phase diagram is presented for arbitrary values of the frustration parameter $\kappa \equiv J_{2}/J_{1}$, and when each of the exchange couplings can take either sign.