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.

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

References in corpus (44)

• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Canonical Typicality
• Low-temperature properties of classical, geometrically frustrated antiferromagnets
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice
• Order versus Disorder in the Quantum Heisenberg Antiferromagnet on the Kagom{é} lattice: an approach through exact spectra analysis
• Macroscopic magnetization jumps due to independent magnons in frustrated quantum spin lattices
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Low-energy sector of the S=1/2 Kagome antiferromagnet
• Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet
• Canonical Thermal Pure Quantum State
• Thermal Pure Quantum States at Finite Temperature
• Frustrated antiferromagnets with entanglement renormalization: ground state of the spin-1/2 Heisenberg model on a kagome lattice
• Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
• Magnetization plateaus in frustrated antiferromagnetic quantum spin models
• Exact low-temperature behavior of kagome antiferromagnet at high fields
• Gapped spin liquid with ${\mathbb{Z}}_2$-topological order for kagome Heisenberg model
• Exact eigenstates and macroscopic magnetization jumps in strongly frustrated spin lattices
• Numerical study of magnetization plateaux in the spin-1/2 kagome Heisenberg antiferromagnet
• Universal low-temperature behavior of frustrated quantum antiferromagnets in the vicinity of the saturation field
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Magnetism of the N=42 kagome lattice antiferromagnet
• Finite low-temperature entropy of some strongly frustrated quantum spin lattices 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
• High field properties of geometrically frustrated magnets
• Properties of highly frustrated magnetic molecules studied by the finite-temperature Lanczos method
• 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
• Magnetic-field induced spin-Peierls instability in strongly frustrated quantum spin lattices
• Quantum kagome antiferromagnet in a magnetic field: Low-lying non-magnetic excitations versus valence-bond crystal order
• Thermodynamic properties of the Shastry-Sutherland model throughout the dimer-product phase
• Numerical Contractor Renormalization Method for Quantum Spin Models
• Lattice gas description of pyrochlore and checkerboard antiferromagnets in a strong magnetic field
• Magnon crystallization in the kagome lattice antiferromagnet
• Sublattice Coding Algorithm and Distributed Memory Parallelization for Large-Scale Exact Diagonalizations of Quantum Many-Body Systems
• From classical to quantum Kagome antiferromagnet in a magnetic field
• Magnetocaloric effect in quantum spin-s chains
• Chiral and Critical Spin Liquids in Spin-$1/2$ Kagome Antiferromagnet
• The ground-state phase diagram of the XXZ spin-s kagome antiferromagnet: A coupled-cluster study
• Linear energy bounds for Heisenberg spin systems
• 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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