Quantum-group-invariant $D^{(2)}_{n+1}$ models: Bethe ansatz and finite-size spectrum
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| Format: | Preprint |
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2025
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| _version_ | 1866915683095281664 |
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| author | Frahm, Holger Gehrmann, Sascha Nepomechie, Rafael I. Retore, Ana L. |
| author_facet | Frahm, Holger Gehrmann, Sascha Nepomechie, Rafael I. Retore, Ana L. |
| contents | 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 $0<γ<π/4$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_00610 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum-group-invariant $D^{(2)}_{n+1}$ models: Bethe ansatz and finite-size spectrum Frahm, Holger Gehrmann, Sascha Nepomechie, Rafael I. Retore, Ana L. High Energy Physics - Theory Statistical Mechanics Mathematical Physics Quantum Physics 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 $0<γ<π/4$, 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. |
| title | Quantum-group-invariant $D^{(2)}_{n+1}$ models: Bethe ansatz and finite-size spectrum |
| topic | High Energy Physics - Theory Statistical Mechanics Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2509.00610 |