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

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.

Main paper (7 pages, 5 figures, 1 table) + Supplemental Material

References in corpus (21)

• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• On the stability of U(1) spin liquids in two dimensions
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Variational Monte Carlo Method Combined with Quantum-Number Projection and Multi-Variable Optimization
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• Competing orders at higher-order Van Hove points
• Valence-bond crystal in the extended kagome spin-1/2 quantum Heisenberg antiferromagnet: A variational Monte Carlo approach
• Frustrated Quantum Spins at finite Temperature: Pseudo-Majorana functional RG approach
• Intertwined nematic orders in a frustrated ferromagnet
• Magnetic field induced quantum spin liquid in the two coupled trillium lattices of K${}_2$Ni${}_2$(SO${}_4$)${}_3$
• Competition between spin liquids and valence-bond order in the frustrated spin-$1/2$ Heisenberg model on the honeycomb lattice
• Nematic and supernematic phases in Kagome quantum antiferromagnets under a magnetic field
• Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
• Gutzwiller-projected states for the $J_1$-$J_2$ Heisenberg model on the kagome lattice: achievements and pitfalls
• $\mathbf{q}=0$ long-range magnetic order in centennialite CaCu${}_3$(OD)${}_6$Cl${}_2$$\cdot$0.6D${}_2$O: A spin-1/2 perfect kagome antiferromagnet with $J_1$-$J_2$-$J_d$
• Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice
• The spin-1/2 Kagome XXZ model in a field: competition between lattice nematic and solid orders
• Dissipative spin dynamics in hot quantum paramagnets
• Self-Optimized Superconductivity Attainable by Interlayer Phase Separation at Cuprate Interfaces

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• Symmetry, Superposition and Fragmentation in Classical Spin Liquids: A General Framework and Applications to Square Kagome Magnets
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