Integrable boundary conditions for staggered vertex models

authored by: Holger Frahm, Sascha Gehrmann
Abstract: Yang-Baxter integrable vertex models with a generic \( \mathbb{Z}_2 \)-staggering can be expressed in terms of composite \(\mathbb{R}\)-matrices given in terms of the elementary \(R\)-matrices. Similarly, integrable open boundary conditions can be constructed through generalized reflection algebras based on these objects and their representations in terms of composite boundary matrices \(\mathbb{K}^\pm\). We show that only two types of staggering yield a local Hamiltonian with integrable open boundary conditions in this approach. The staggering in the underlying model allows for a second hierarchy of commuting integrals of motion (in addition to the one including the Hamiltonian obtained from the usual transfer matrix), starting with the so-called quasi momentum operator. In this paper, we show that this quasi momentum operator can be obtained together with the Hamiltonian for both periodic and open models in a unified way from enlarged Yang-Baxter or reflection algebras in the composite picture. For the special case of the staggered six-vertex model, this allows constructing an integrable spectral flow between the two local cases.
Organisation(s): Institute of Theoretical Physics
Type: Article
Journal: Journal of Physics A: Mathematical and Theoretical
Volume: 56
No. of pages: 32
ISSN: 1751-8113
Publication date: 26.01.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Physics and Astronomy(all), Statistical and Nonlinear Physics, Statistics and Probability, Mathematical Physics, Modelling and Simulation
Electronic version(s): https://doi.org/10.48550/arXiv.2209.06182 (Access: Open)
https://doi.org/10.1088/1751-8121/acb29f (Access: Open)

BibTeX

@article{df24b7f173684cb3b54de49f40bda864,
title = "Integrable boundary conditions for staggered vertex models",
abstract = "Yang-Baxter integrable vertex models with a generic \( \mathbb{Z}_2 \)-staggering can be expressed in terms of composite \(\mathbb{R}\)-matrices given in terms of the elementary \(R\)-matrices. Similarly, integrable open boundary conditions can be constructed through generalized reflection algebras based on these objects and their representations in terms of composite boundary matrices \(\mathbb{K}^\pm\). We show that only two types of staggering yield a local Hamiltonian with integrable open boundary conditions in this approach. The staggering in the underlying model allows for a second hierarchy of commuting integrals of motion (in addition to the one including the Hamiltonian obtained from the usual transfer matrix), starting with the so-called quasi momentum operator. In this paper, we show that this quasi momentum operator can be obtained together with the Hamiltonian for both periodic and open models in a unified way from enlarged Yang-Baxter or reflection algebras in the composite picture. For the special case of the staggered six-vertex model, this allows constructing an integrable spectral flow between the two local cases.",
keywords = "Bethe Ansatz, boundary conditions, finite-size scaling, integrability, spectral flow, staggering, vertex models",
author = "Holger Frahm and Sascha Gehrmann",
note = "Funding Information: Funding for this work has been provided by the Deutsche Forschungsgemeinschaft under Grant No. Fr 737/9-2 as part of the research unit Correlations in Integrable Quantum Many-Body Systems (FOR2316).",
year = "2023",
month = jan,
day = "26",
doi = "10.48550/arXiv.2209.06182",
language = "English",
volume = "56",
journal = "Journal of Physics A: Mathematical and Theoretical",
issn = "1751-8113",
publisher = "IOP Publishing Ltd.",
number = "2",
}