Integrable boundary conditions for staggered vertex models

Research output: Contribution to journal › Article › Research › peer review

Authors

Research Organisations

View graph of relations

Details

Original languageEnglish
Article number025001
Number of pages32
JournalJournal of Physics A: Mathematical and Theoretical
Volume56
Issue number2
Publication statusPublished - 26 Jan 2023

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

ASJC Scopus subject areas

Cite this

Integrable boundary conditions for staggered vertex models. / Frahm, Holger; Gehrmann, Sascha.
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

Frahm, H & Gehrmann, S 2023, 'Integrable boundary conditions for staggered vertex models', Journal of Physics A: Mathematical and Theoretical, vol. 56, no. 2, 025001. https://doi.org/10.48550/arXiv.2209.06182, https://doi.org/10.1088/1751-8121/acb29f
Frahm, H., & Gehrmann, S. (2023). Integrable boundary conditions for staggered vertex models. Journal of Physics A: Mathematical and Theoretical, 56(2), Article 025001. https://doi.org/10.48550/arXiv.2209.06182, https://doi.org/10.1088/1751-8121/acb29f
Frahm H, Gehrmann S. Integrable boundary conditions for staggered vertex models. Journal of Physics A: Mathematical and Theoretical. 2023 Jan 26;56(2):025001. doi: 10.48550/arXiv.2209.06182, 10.1088/1751-8121/acb29f
Frahm, Holger ; Gehrmann, Sascha. / Integrable boundary conditions for staggered vertex models. In: Journal of Physics A: Mathematical and Theoretical. 2023 ; Vol. 56, No. 2.
Download
@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",
number = "2",

}

Download

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 -

By the same author(s)

  1. Finite-size spectrum of the staggered six-vertex model with antidiagonal boundary conditions

    Research output: Contribution to journal › Article › Research › peer review

  2. Scaling limit of the staggered six-vertex model with \(U_q(\mathfrak{sl}(2))\) invariant boundary conditions

    Research output: Contribution to journal › Article › Research › peer review

  3. The D(2)3 spin chain and its finite-size spectrum

    Research output: Contribution to journal › Article › Research › peer review

  4. Uq[OSp(3|2)] quantum chains with quantum group invariant boundaries

    Research output: Contribution to journal › Article › Research › peer review

  5. Factorization of density matrices in the critical RSOS models

    Research output: Contribution to journal › Article › Research › peer review