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- W4385262024 abstract "For the quantum Heisenberg antiferromagnet with spin-$j$ on a bipartite, balanced graph, the Lieb-Mattis theorem, ``Ordering of energy levels,'' guarantees that the ground state is a spin singlet, and moreover, defining $E^{textrm{AF}}_{min}(S)$ to be the minimum eigenvalue of the Hamiltonian in the invariant subspace consisting of all spin $S$ vectors, $boldsymbol{S}_{mathrm{tot}}^2 psi = S(S+1)psi$, the function $E^{textrm{AF}}_{min}(S)$ is monotonically increasing for $0leq Sleq j|mathcal{V}|$. For the ferromagnet, the absolute ground state is $E_{min}^{textrm{FM}}(j|mathcal{V}|)$. We say that the graph satisfies ``ferromagnetic ordering of energy levels'' at order $n$, or FOEL-$n$, if two properties hold: (1) $E_{min}^{textrm{FM}}(j|mathcal{V}|)leq dots leq E_{min}^{mathrm{FM}}(j|mathcal{V}|-n)$, and (2) $E_{min}^{mathrm{FM}}(j|mathcal{V}|-n)leq E_{min}^{mathrm{FM}}(j|mathcal{V}|-m)$ for all $mgeq n$. Caputo, Liggett and Richthammer proved a theorem which generally implies FOEL-$1$ is true. Apparently $E_0^{mathrm{FM}}(0) <E_0^{mathrm{FM}}(1)$ for sufficiently long spin rings, $mathbb{Z}/Lmathbb{Z}$ with even length $L$. So FOEL-$n$ does not hold for $n=jL-1$. We consider $E_0^{mathrm{FM}}(1)-E_0^{mathrm{FM}}(0)$ using linear spin-wave analysis and numerical computation. Using the Bethe ansatz, Sutherland already considered the spin ring with $j=1/2$ and notably proved weak paramagnetism. But we also present evidence for $j>1/2$." @default.
- W4385262024 created "2023-07-26" @default.
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- W4385262024 date "2023-07-24" @default.
- W4385262024 modified "2023-09-25" @default.
- W4385262024 title "Violation of Ferromagnetic Ordering of Energy Levels in Spin Rings by Weak Paramagnetism of the Singlet" @default.
- W4385262024 doi "https://doi.org/10.48550/arxiv.2307.12773" @default.
- W4385262024 hasPublicationYear "2023" @default.
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