TY - JOUR

T1 - Integrable boundary conditions for staggered vertex models

AU - Frahm, Holger

AU - Gehrmann, Sascha

N1 - 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).

PY - 2023/1/26

Y1 - 2023/1/26

N2 - 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.

AB - 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.

KW - Bethe Ansatz

KW - boundary conditions

KW - finite-size scaling

KW - integrability

KW - spectral flow

KW - staggering

KW - vertex models

UR - http://www.scopus.com/inward/record.url?scp=85147225804&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2209.06182

DO - 10.48550/arXiv.2209.06182

M3 - Article

VL - 56

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 2

M1 - 025001

ER -