## Details

Original language | English |
---|---|

Article number | 083104 |

Number of pages | 21 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Volume | 2023 |

Publication status | Published - 22 Aug 2023 |

## Abstract

We study reduced density matrices of the integrable critical restricted solid-on-solid (RSOS) model in a particular topological sector containing the ground state. Similar as in the spin- 1/2 Heisenberg model it has been observed that correlation functions of this model on short segments can be 'factorized': they are completely determined by a single nearest-neighbour two-point function ω and a set of structure functions. While ω captures the dependence on the system size and the state of the system the structure functions can be expressed in terms of the possible operators on the segment, in the present case representations of the Temperley-Lieb algebra TLn, and are independent of the model parameters. We present explicit results for the function ω in the infinite system ground state of the model and compute multi-point local height probabilities for up to four adjacent sites for the RSOS model and the related three-point correlation functions of non-Abelian su(2)k anyons.

## Keywords

- factorization of correlation functions, interaction-round-a-face models, reduced q-Knizhnik-Zamolodchikov equation, Temperley-Lieb algebra, Yang-Baxter integrability

## ASJC Scopus subject areas

- Physics and Astronomy(all)
**Condensed Matter Physics**- Physics and Astronomy(all)
**Statistical and Nonlinear Physics**- Mathematics(all)
**Mathematical Physics**- Mathematics(all)
**Statistics and Probability**- Decision Sciences(all)
**Statistics, Probability and Uncertainty**

## Cite this

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**Factorization of density matrices in the critical RSOS models.**/ Westerfeld, Daniel; Großpietsch, Maxime; Kakuschke, Hannes et al.

In: Journal of Statistical Mechanics: Theory and Experiment, Vol. 2023, 083104, 22.08.2023.

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

*Journal of Statistical Mechanics: Theory and Experiment*, vol. 2023, 083104. https://doi.org/10.1088/1742-5468/aceeef

*Journal of Statistical Mechanics: Theory and Experiment*,

*2023*, Article 083104. https://doi.org/10.1088/1742-5468/aceeef

}

TY - JOUR

T1 - Factorization of density matrices in the critical RSOS models

AU - Westerfeld, Daniel

AU - Großpietsch, Maxime

AU - Kakuschke, Hannes

AU - Frahm, Holger

N1 - Funding Information: The authors thank Alexi Morin Duchesne and Frank Göhmann for valuable discussions. This work is part of the programme of the research unit “Correlations in Integrable Quantum Many-Body Systems” (FOR 2316) funded by the Deutsche Forschungsgemeinschaft.

PY - 2023/8/22

Y1 - 2023/8/22

N2 - We study reduced density matrices of the integrable critical restricted solid-on-solid (RSOS) model in a particular topological sector containing the ground state. Similar as in the spin- 1/2 Heisenberg model it has been observed that correlation functions of this model on short segments can be 'factorized': they are completely determined by a single nearest-neighbour two-point function ω and a set of structure functions. While ω captures the dependence on the system size and the state of the system the structure functions can be expressed in terms of the possible operators on the segment, in the present case representations of the Temperley-Lieb algebra TLn, and are independent of the model parameters. We present explicit results for the function ω in the infinite system ground state of the model and compute multi-point local height probabilities for up to four adjacent sites for the RSOS model and the related three-point correlation functions of non-Abelian su(2)k anyons.

AB - We study reduced density matrices of the integrable critical restricted solid-on-solid (RSOS) model in a particular topological sector containing the ground state. Similar as in the spin- 1/2 Heisenberg model it has been observed that correlation functions of this model on short segments can be 'factorized': they are completely determined by a single nearest-neighbour two-point function ω and a set of structure functions. While ω captures the dependence on the system size and the state of the system the structure functions can be expressed in terms of the possible operators on the segment, in the present case representations of the Temperley-Lieb algebra TLn, and are independent of the model parameters. We present explicit results for the function ω in the infinite system ground state of the model and compute multi-point local height probabilities for up to four adjacent sites for the RSOS model and the related three-point correlation functions of non-Abelian su(2)k anyons.

KW - factorization of correlation functions

KW - interaction-round-a-face models

KW - reduced q-Knizhnik-Zamolodchikov equation

KW - Temperley-Lieb algebra

KW - Yang-Baxter integrability

UR - http://www.scopus.com/inward/record.url?scp=85169559337&partnerID=8YFLogxK

U2 - 10.1088/1742-5468/aceeef

DO - 10.1088/1742-5468/aceeef

M3 - Article

VL - 2023

JO - Journal of Statistical Mechanics: Theory and Experiment

JF - Journal of Statistical Mechanics: Theory and Experiment

SN - 1742-5468

M1 - 083104

ER -