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

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.

published version; 17 pages of text including 10 figures and Ukrainian abstract

References in corpus (15)

• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Magnetization plateaus in frustrated antiferromagnetic quantum spin models
• Exact low-temperature behavior of kagome antiferromagnet at high fields
• Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices
• Universal low-temperature behavior of frustrated quantum antiferromagnets in the vicinity of the saturation field
• Frustrated two dimensional quantum magnets
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice
• Universal properties of highly frustrated quantum magnets in strong magnetic fields
• Quantum kagome antiferromagnet in a magnetic field: Low-lying non-magnetic excitations versus valence-bond crystal order
• Numerical Contractor Renormalization Method for Quantum Spin Models
• Magnon crystallization in the kagome lattice antiferromagnet
• The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
• Thermodynamic properties of an $S=1/2$ ring-exchange model on the triangular lattice
• Chemistry of the spin-1/2 kagome Heisenberg antiferromagnet

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