Scaling limit of the staggered six-vertex model with \(U_q(\mathfrak{sl}(2))\) invariant boundary conditions

authored by: Holger Frahm, Sascha Gehrmann, Gleb Andreevich Kotousov
Abstract: We study the scaling limit of a statistical system, which is a special case of the integrable inhomogeneous six-vertex model. It possesses \(U_q(\mathfrak{sl}(2))\) invariance due to the choice of open boundary conditions imposed. An interesting feature of the lattice theory is that the spectrum of scaling dimensions contains a continuous component. By applying the ODE/IQFT correspondence and the method of the Baxter \(Q\) operator the corresponding density of states is obtained. In addition, the partition function appearing in the scaling limit of the lattice model is computed, which may be of interest for the study of nonrational CFTs in the presence of boundaries. As a side result of the research, a simple formula for the matrix elements of the \(Q\) operator for the general, integrable, inhomogeneous six-vertex model was discovered, that has not yet appeared in the literature. It is valid for a certain one parameter family of diagonal open boundary conditions in the sector with the z-projection of the total spin operator being equal to zero.
Organisation(s): Institute of Theoretical Physics
Type: Article
Journal: SciPost Physics
Volume: 16
No. of pages: 34
Publication date: 05.06.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Nuclear and High Energy Physics, Condensed Matter Physics, Mathematical Physics
Electronic version(s): https://arxiv.org/abs/2312.11238 (Access: Open)
https://doi.org/10.21468/SciPostPhys.16.6.149 (Access: Open)

BibTeX

@article{1864a95976514a20a84dcb0d2e3c316c,
title = "Scaling limit of the staggered six-vertex model with \(U_q(\mathfrak{sl}(2))\) invariant boundary conditions",
abstract = "We study the scaling limit of a statistical system, which is a special case of the integrable inhomogeneous six-vertex model. It possesses \(U_q(\mathfrak{sl}(2))\) invariance due to the choice of open boundary conditions imposed. An interesting feature of the lattice theory is that the spectrum of scaling dimensions contains a continuous component. By applying the ODE/IQFT correspondence and the method of the Baxter \(Q\) operator the corresponding density of states is obtained. In addition, the partition function appearing in the scaling limit of the lattice model is computed, which may be of interest for the study of nonrational CFTs in the presence of boundaries. As a side result of the research, a simple formula for the matrix elements of the \(Q\) operator for the general, integrable, inhomogeneous six-vertex model was discovered, that has not yet appeared in the literature. It is valid for a certain one parameter family of diagonal open boundary conditions in the sector with the z-projection of the total spin operator being equal to zero. ",
author = "Holger Frahm and Sascha Gehrmann and Kotousov, {Gleb Andreevich}",
note = "Publisher Copyright: Copyright H. Frahm et al.",
year = "2024",
month = jun,
day = "5",
doi = "10.21468/SciPostPhys.16.6.149",
language = "English",
volume = "16",
journal = "SciPost Physics",
issn = "2542-4653",
publisher = "SciPost Foundation",
number = "6",
}