Linear independence of localized magnon states

Abstract

At the magnetic saturation field, certain frustrated lattices have a class of states known as "localized multi-magnon states" as exact ground states. The number of these states scales exponentially with the number $N$ of spins and hence they have a finite entropy also in the thermodynamic limit $N\to \infty$ provided they are sufficiently linearly independent. In this article we present rigorous results concerning the linear dependence or independence of localized magnon states and investigate special examples. For large classes of spin lattices including what we called the orthogonal type and the isolated type as well as the kagomé, the checkerboard and the star lattice we have proven linear independence of all localized multi-magnon states. On the other hand the pyrochlore lattice provides an example of a spin lattice having localized multi-magnon states with considerable linear dependence.

23 pages, 6 figures

References in corpus (6)

• Enhanced magnetocaloric effect in frustrated magnets
• Exact low-temperature behavior of kagome antiferromagnet at high fields
• Universal low-temperature behavior of frustrated quantum antiferromagnets in the vicinity of the saturation field
• Absence of magnetic order for the spin-half Heisenberg antiferromagnet on the star lattice
• Quantum kagome antiferromagnet in a magnetic field: Low-lying non-magnetic excitations versus valence-bond crystal order
• Effective Hamiltonian for the Pyrochlore antiferromagnet: semiclassical derivation and degeneracy

Cited by in corpus (9)

• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Universal properties of highly frustrated quantum magnets in strong magnetic fields
• Finite-temperature order-disorder phase transition in a frustrated bilayer quantum Heisenberg antiferromagnet in strong magnetic fields
• Low-temperature thermodynamics for a flat-band ferromagnet: Rigorous versus numerical results
• The sawtooth chain: From Heisenberg spins to Hubbard electrons
• Exact low-temperature properties of a class of highly frustrated Hubbard models
• Frustration effects in antiferromagnetic molecules: the cuboctahedron
• Spin-wave spectra of a kagome stripe
• Low-temperature thermodynamics of one class of flat-band models