Details
| Original language | English |
|---|---|
| Article number | 025001 |
| Number of pages | 32 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 56 |
| Issue number | 2 |
| Publication status | Published - 26 Jan 2023 |
Abstract
Keywords
- Bethe Ansatz, boundary conditions, finite-size scaling, integrability, spectral flow, staggering, vertex models
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- Mathematical Physics
- Mathematics(all)
- Modelling and Simulation
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In: Journal of Physics A: Mathematical and Theoretical, Vol. 56, No. 2, 025001, 26.01.2023.
Research output: Contribution to journal › Article › Research › peer review
}
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 -