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

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• Exact low-temperature properties of a class of highly frustrated Hubbard models
• Enhancement of magnetization plateaus in low dimensional spin systems
• Flat-band physics in the spin-1/2 sawtooth chain
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• Magnetization plateaus of spin-$\frac{1}{2}$ system on a 5/7 skewed ladder
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• A frustrated spin-1/2 Heisenberg antiferromagnet on a chevron-square lattice
• Bose-Hubbard model on two-dimensional line graphs
• Non-ergodic one-magnon magnetization dynamics of the antiferromagnetic delta chain
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• Hard-core bosons in flat band systems above the critical density
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• Weak ergodicity breaking with isolated integrable sectors
• Spin-wave spectra of a kagome stripe
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• On flat bands in the $J_1$-$J_2$-$J_3$ XXZ sawtooth chain
• Non-ergodic one-magnon magnetization dynamics of the kagome lattice antiferromagnet
• Magnetic anisotropy effect on stabilizing magnetization plateaus of kagome strip chain Heisenberg antiferromagnets