Abstract
The high-field regime of the spin-s XXZ antiferromagnet on the kagome lattice gives rise to macroscopically degenerate ground states thanks to a completely flat lowest single-magnon band. The corresponding excitations can be localized on loops in real space and have been coined "localized magnons". Thus, the description of the many-body ground states amounts to characterizing the allowed classical loop configurations and eliminating the quantum mechanical linear relations between them. Here, we investigate this loop-gas description on finite kagome lattices with open boundary conditions and compare the results with exact diagonalization for the spin-1/2 XY model on the same lattice. We find that the loop gas provides an exact account of the degenerate ground-state manifold while a hard-hexagon description misses contributions from nested loop configurations. The densest packing of the loops corresponds to a magnon crystal that according to the zero-temperature magnetization curve is a stable ground state of the spin-1/2 XY model in a window of magnetic fields of about 4% of the saturation field just below this saturation field. We also present numerical results for the specific heat obtained by the related methods of thermal pure quantum (TPQ) states and the finite-temperature Lanczos method (FTLM). For a field in the stability range of the magnon crystal, one finds a low-temperature maximum of the specific heat that corresponds to a finite-temperature phase transition into the magnon crystal at low temperatures.
Highlights
The study of the kagome lattice in condensed matter physics goes back at least to Syôzi’s famous investigation of the Ising model on this lattice [1]
We present numerical results for the specific heat obtained by the related methods of thermal pure quantum (TPQ) states and the finite-temperature Lanczos method (FTLM)
We have first reviewed the localized-magnon states that appear as ground states in the high-field regime of the spin-s XXZ model on the kagome lattice [31,32,33,34,35,36,37]
Summary
The study of the kagome lattice in condensed matter physics goes back at least to Syôzi’s famous investigation of the Ising model on this lattice [1]. The connectivity of the corner-sharing arrangement is low so that the number of constraints arising from the coupling between triangles is low (see, e.g., reference [2]) This entails a huge degeneracy of the Ising antiferromagnet on the kagome lattice [3] and preempts any finite-temperature phase transition in this case [1]. One finds that the number of linearly independent loop configurations does not describe all ground states of the spin-1/2 kagome Heisenberg antiferromagnet on a torus [42] which raises the question whether the loop gas does yield a complete description of the ground-state manifold of the spin-1/2 kagome Heisenberg antiferromagnet around the saturation field in the thermodynamic limit The latter question urges us to investigate here the loop gas on finite systems with open boundary conditions. We analyze the resulting thermodynamic properties and present a comparison with “exact” diagonalization results for the spin-1/2 XY model
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