Abstract
In this paper, we do a complete classification of valence-bond crystals (VBCs) on the kagomé lattice based on general arguments of symmetry only and thus identify many new VBCs for different unit cell sizes. For the spin-1/2 Heisenberg antiferromagnet, we study the relative energetics of competing gapless spin liquids (SLs) and VBC phases within the class of Gutzwiller-projected fermionic wave functions using variational Monte Carlo techniques, hence implementing exactly the constraint of one fermion per site. By using a state-of-the-art optimization method, we conclusively show that the U(1) Dirac SL is remarkably stable towards dimerizing into all 6-, 12- and 36-site unit cell VBCs. This stability is also preserved on addition of a next-nearest-neighbor super-exchange coupling of both antiferromagnetic and ferromagnetic (FM) type. However, we find that a 36-site unit cell VBC is stabilized on addition of a very small next-nearest-neighbor FM super-exchange coupling, i.e. |J2| ≈ 0.045, and this VBC is the same in terms of space-group symmetry as that obtained in an effective quantum dimer model study. It breaks reflection symmetry, has a nontrivial flux pattern and is a strong dimerization of the uniform RVB SL.
Highlights
For many decades, physicists have been actively searching for playgrounds that are ‘hot’ enough to melt magnetic freezing at temperatures well below the characteristic interaction energy scales in the system
We study the energetics of spin liquids (SLs) and valence-bond crystals (VBCs) phases for the spin-1/2 quantum Heisenberg antiferromagnet (QHAF) using Gutzwiller projected fermionic wave functions with the variational quantum Monte Carlo technique
We introduce an amplitude modulation of χij consistent with the symmetries of the VBC, i.e. bonds belonging to the same class have the same amplitude, which is set to different values for different classes
Summary
Physicists have been actively searching for playgrounds that are ‘hot’ enough to melt magnetic freezing at temperatures well below the characteristic interaction energy scales in the system. A more recent generalized QDM study found a new (possibly chiral) VBC of 12-site unit cell to be competing with the 36-site unit cell VBC It established an extensive quasi-degeneracy of the ground state manifold of the kagome S = 1/2 QHAF with a stiff competition between several phases [55]. In section 3.1.2, we show that a broken symmetry phase is stabilized on addition of a small NNN FM coupling, which is consistent with the findings in [59] This VBC has a 36-site unit cell with a nontrivial flux pattern threading its plaquettes and it is found to be a strong dimerization of another competing U(1) gapless SL, the so-called uniform RVB SL [32]. This feature is especially important for the spin-1/2 QHAF since the energies of all the competing phases are rather close
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