Integrable boundary conditions for staggered vertex models

verfasst von
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.

Organisationseinheit(en)
Institut für Theoretische Physik
Typ
Artikel
Journal
Journal of Physics A: Mathematical and Theoretical
Band
56
Anzahl der Seiten
32
ISSN
1751-8113
Publikationsdatum
26.01.2023
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
ASJC Scopus Sachgebiete
Physik und Astronomie (insg.), Statistische und nichtlineare Physik, Statistik und Wahrscheinlichkeit, Mathematische Physik, Modellierung und Simulation
Elektronische Version(en)
https://doi.org/10.48550/arXiv.2209.06182 (Zugang: Offen)
https://doi.org/10.1088/1751-8121/acb29f (Zugang: Offen)