Factorization of density matrices in the critical RSOS models

authored by: Daniel Westerfeld, Maxime Großpietsch, Hannes Kakuschke, Holger Frahm
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.
Organisation(s): Institute of Theoretical Physics
Type: Article
Journal: Journal of Statistical Mechanics: Theory and Experiment
Volume: 2023
No. of pages: 21
ISSN: 1742-5468
Publication date: 22.08.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Condensed Matter Physics, Statistical and Nonlinear Physics, Mathematical Physics, Statistics and Probability, Statistics, Probability and Uncertainty
Electronic version(s): https://arxiv.org/abs/2303.15252 (Access: Open)
https://doi.org/10.1088/1742-5468/aceeef (Access: Open)

BibTeX

@article{5bb356c46d64417884d55d7d0b7ccc4d,
title = "Factorization of density matrices in the critical RSOS models",
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",
author = "Daniel Westerfeld and Maxime Gro{\ss}pietsch and Hannes Kakuschke and Holger Frahm",
note = "Funding Information: The authors thank Alexi Morin Duchesne and Frank G{\"o}hmann 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.",
year = "2023",
month = aug,
day = "22",
doi = "10.1088/1742-5468/aceeef",
language = "English",
volume = "2023",
journal = "Journal of Statistical Mechanics: Theory and Experiment",
issn = "1742-5468",
publisher = "IOP Publishing Ltd.",
}