Finite size spectrum of the staggered six-vertex model with \(U_q(sl(2))\)-invariant boundary conditions

authored by: Holger Frahm, Sascha Gehrmann
Abstract: The finite size spectrum of the critical \(\mathbb{Z}_2\)-staggered spin-1/2 XXZ model with quantum group invariant boundary conditions is studied. For a particular (self-dual) choice of the staggering the spectrum of conformal weights of this model has been recently been shown to have a continuous component, similar as in the model with periodic boundary conditions whose continuum limit has been found to be described in terms of the non-compact \(SU(2,\mathbb{R})/U(1)\) Euclidean black hole conformal field theory (CFT). Here we show that the same is true for a range of the staggering parameter. In addition we find that levels from the discrete part of the spectrum of this CFT emerge as the anisotropy is varied. The finite size amplitudes of both the continuous and the discrete levels are related to the corresponding eigenvalues of a quasi-momentum operator which commutes with the Hamiltonian and the transfer matrix of the model.
Organisation(s): Institute of Theoretical Physics
Type: Article
Journal: Journal of High Energy Physics
Volume: 2022
No. of pages: 32
ISSN: 1029-8479
Publication date: 14.01.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Nuclear and High Energy Physics
Electronic version(s): http://arxiv.org/abs/2111.00850 (Access: Open)
https://doi.org/10.1007/JHEP01(2022)070 (Access: Open)

BibTeX

@article{7e65ce7ca1f1470a83afcc3467f47a2d,
title = "Finite size spectrum of the staggered six-vertex model with \(U_q(sl(2))\)-invariant boundary conditions",
abstract = " The finite size spectrum of the critical \(\mathbb{Z}_2\)-staggered spin-1/2 XXZ model with quantum group invariant boundary conditions is studied. For a particular (self-dual) choice of the staggering the spectrum of conformal weights of this model has been recently been shown to have a continuous component, similar as in the model with periodic boundary conditions whose continuum limit has been found to be described in terms of the non-compact \(SU(2,\mathbb{R})/U(1)\) Euclidean black hole conformal field theory (CFT). Here we show that the same is true for a range of the staggering parameter. In addition we find that levels from the discrete part of the spectrum of this CFT emerge as the anisotropy is varied. The finite size amplitudes of both the continuous and the discrete levels are related to the corresponding eigenvalues of a quasi-momentum operator which commutes with the Hamiltonian and the transfer matrix of the model. ",
keywords = "cond-mat.stat-mech, hep-th, math-ph, math.MP, Lattice Integrable Models, Conformal Field Theory, Bethe Ansatz",
author = "Holger Frahm and Sascha Gehrmann",
year = "2022",
month = jan,
day = "14",
doi = "10.1007/JHEP01(2022)070",
language = "English",
volume = "2022",
journal = "Journal of High Energy Physics",
issn = "1029-8479",
publisher = "Springer Verlag",
number = "1",
}