Pinch-points to half-moons and up in the stars: the kagome skymap

TL;DR

This study investigates how non-analytic features like half-moons and stars in the spin structure factor evolve in a kagome lattice Heisenberg antiferromagnet as quantum fluctuations and couplings change, revealing a transition from a Dirac spin liquid to ordered phases.

Contribution

It provides the first detailed analysis of the fate of half-moons and star features in the kagome antiferromagnet with varying couplings, using multiple advanced numerical methods.

Findings

Dirac spin liquid remains stable up to intermediate couplings.

Half-moons appear in the structure factor near the transition to valence bond crystal.

At larger couplings, the system develops star-like magnetic order.

Abstract

Pinch point singularities, associated with flat band magnetic excitations, are tell-tale signatures of Coulomb spin liquids. While their properties in the presence of quantum fluctuations have been widely studied, the fate of the complementary non-analytic features -- shaped as half-moons and stars -- arising from adjacent shallow dispersive bands has remained unexplored. Here, we address this question for the spin $S=1/2$ Heisenberg antiferromagnet on the kagome lattice with second and third neighbor couplings, which allows one to tune the classical ground state from flat bands to being governed by shallow dispersive bands for intermediate coupling strengths. Employing the complementary strengths of variational Monte Carlo, pseudo-fermion functional renormalization group, and density-matrix renormalization group, we establish the quantum phase diagram. The U(1) Dirac spin liquid ground state of the nearest-neighbor antiferromagnet remains remarkably robust till intermediate coupling strengths when it transitions into a pinwheel valence bond crystal displaying signatures of half-moons in its structure factor. Our work thus identifies a microscopic setting that realizes one of the proximate orders of the Dirac spin liquid identified in a recent work [Song, Wang, Vishwanath, He, Nat. Commun. 10, 4254 (2019)]. For larger couplings, we obtain a collinear magnetically ordered ground state characterized by star-like patterns.