Abstract
The spin-1/2 Heisenberg kagome antiferromagnet is one of the paradigmatic playgrounds for frustrated quantum magnetism, with an extensive number of competing resonating valence bond (RVB) states emerging at low energies, including gapped and gapless spin liquids and valence bond crystals. Here we revisit the crossover from this quantum RVB phase to a semiclassical regime brought about by anisotropic Kitaev interactions, and focus on the precise mechanisms underpinning this crossover. To this end, we introduce a simple parametrization of the classical ground states (GSs) in terms of emergent Ising-like variables, and use this parametrizaton: i) to construct an effective low-energy description of the order-by-disorder mechanism operating in a large part of the phase diagram, and ii) to contrast, side by side, exact diagonalization data obtained from the full basis with that obtained from the restricted (orthonormalized) basis of classical GSs. The results reveal that fluctuation corrections from states outside the restricted basis are strongly quenched inside the semiclassical regime (due to the large anisotropy spin gaps), and that the RVB phase survives up to a relatively large value of Kitaev anisotropy $K$. We further find that the pure Kitaev model admits a subextensive number of one-dimensional symmetries, which explains naturally the absence of classical and quantum order by disorder reported previously.
Highlights
In recent years, quantum materials with strong spin-orbit coupled 4d and 5d ions and bond-dependent anisotropic interactions have been the subject of much experimental and theoretical work [1,2,3,4,5,6,7,8,9]
We demonstrate explicitly the quantum-classical crossover between the resonating valence bond (RVB) physics of the kagome Heisenberg antiferromagnet (KHAF) and the regime stabilized by Kitaev anisotropy
Our exact diagonalizations (ED) results show a clear quantum-classical crossover from the RVB physics of the Heisenberg antiferromagnet to the regime stabilized by Kitaev anisotropy
Summary
Quantum materials with strong spin-orbit coupled 4d and 5d ions and bond-dependent anisotropic interactions have been the subject of much experimental and theoretical work [1,2,3,4,5,6,7,8,9]. The JK model on the kagome lattice has been studied previously by Kimchi and Vishwanath [22] and by Morita et al [31,32], and a lot of results are already known, including most of the aspects of the classical ground state (GS) phase diagram [22,31], a numerical demonstration of an order by disorder mechanism operating in a large part of the parameter space, and the absence of this mechanism in the pure Kitaev model [31]. The comparison shows that the regime stabilized by the Kitaev coupling has a robust semiclassical character, meaning that the fluctuation (e.g., spin-wave) corrections from states outside the restricted basis are heavily quenched by the large anisotropy spin gaps This shows that the RVB phase remains stable in an extended range of parameters, irrespective of the actual nature of the ground state of the KHAF or the presence of a gap.
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