Pinwheel valence-bond-crystal ground state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice

TL;DR

This paper demonstrates that the ground state of the spin-1/2 Heisenberg antiferromagnet on the shuriken lattice is a pinwheel valence-bond crystal, identified through advanced numerical methods revealing a quantum paramagnetic phase with specific VBC order.

Contribution

It provides the first detailed numerical evidence that a pinwheel VBC state emerges as the lowest-energy ground state, originating from a U(1) Dirac spin liquid instability.

Findings

Pinwheel VBC identified as the ground state.

Quantum paramagnetic ground state confirmed.

VBC arises from U(1) Dirac spin liquid instability.

Abstract

We investigate the nature of the ground-state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice by complementary state-of-the-art numerical techniques, such as variational Monte Carlo (VMC) with versatile Gutzwiller-projected Jastrow wave functions, unconstrained multi-variable variational Monte Carlo (mVMC), and pseudo-fermion/Majorana functional renormalization group (PF/PM-FRG) methods. We establish the presence of a quantum paramagnetic ground state and investigate its nature, by classifying symmetric and chiral quantum spin liquids, and inspecting their instabilities towards competing valence-bond-crystal (VBC) orders. Our VMC analysis reveals that a VBC with a pinwheel structure emerges as the lowest-energy variational ground state, and it is obtained as an instability of the U(1) Dirac spin liquid. Analogous conclusions are drawn from mVMC calculations employing accurate BCS pairing states supplemented by symmetry projectors, which confirm the presence of pinwheel VBC order by a thorough analysis of dimer-dimer correlation functions. Our work highlights the nontrivial role of quantum fluctuations via the Gutzwiller projector in resolving the subtle interplay between competing orders.