Quantum-group-invariant $D^{(2)}_{n+1}$ models: Bethe ansatz and finite-size spectrum

• URL: http://arxiv.org/abs/2509.00610v3
• Date: Wed, 29 Oct 2025 12:59:54 GMT
• Title: Quantum-group-invariant $D^{(2)}_{n+1}$ models: Bethe ansatz and finite-size spectrum
• Abstract summary: We consider the quantum integrable spin chain models associated with the Jimbo R-matrix based on the quantum affine algebra $D(2)_n+1$.<n>We find that the symmetry of the lattice model is spontaneously broken, and the spectrum of conformal weights has both discrete and continuous components.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider the quantum integrable spin chain models associated with the Jimbo R-matrix based on the quantum affine algebra $D^{(2)}_{n+1}$, subject to quantum-group-invariant boundary conditions parameterized by two discrete variables $p=0,\dots, n$ and $\varepsilon = 0, 1$. We develop the analytical Bethe ansatz for the previously unexplored case $\varepsilon = 1$ with any $n$, and use it to investigate the effects of different boundary conditions on the finite-size spectrum of the quantum spin chain based on the rank-$2$ algebra $D^{(2)}_3$. Previous work on this model with periodic boundary conditions has shown that it is critical for the range of anisotropy parameters $0<\gamma<\pi/4$, where its scaling limit is described by a non-compact CFT with continuous degrees of freedom related to two copies of the 2D black hole sigma model. The scaling limit of the model with quantum-group-invariant boundary conditions depends on the parameter $\varepsilon$: similarly as in the rank-$1$ $D^{(2)}_2$ chain, we find that the symmetry of the lattice model is spontaneously broken, and the spectrum of conformal weights has both discrete and continuous components, for $\varepsilon=1$. For $p=1$, the latter coincides with that of the $D^{(2)}_2$ chain, which should correspond to a non-compact brane related to one black hole CFT in the presence of boundaries. For $\varepsilon=0$, the spectrum of conformal weights is purely discrete.

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