Loop-gas description of the localized-magnon states on the kagome lattice with open boundary conditions

Abstract

The high-1eld regime of the spin-s XXZ antiferromagnet on the kagome lattice gives rise to macroscopically degenerate ground states thanks to a completely 2at lowest single-magnon band. The corresponding excitations can be localized on loops in real space and have been coined “ localized magnons ” many-body ground states amounts to characterizing the allowed classical loop con1gurations and eliminating the quantum mechanical linear relations between them. Here, we investigate this loop-gas description on 1nite 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 1nd that the loop gas provides an exact account of the degenerate ground-state manifold while a hard-hexagon description misses contributions from nested loop con1gurations. 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 1elds of about 4% of the saturation 1eld just below this saturation 1eld. We also present numerical results for the speci1c heat obtained by the related methods of thermal pure quantum (TPQ) states and the 1nite-temperature Lanczos method (FTLM). For a 1eld in the stability range of the magnon crystal, one 1nds a low-temperature maximum of the speci1c heat that corresponds to a 1nite-temperature phase transition into the magnon crystal at low temperatures.