Density matrices in integrable face models

authored by: Holger Frahm, Daniel Westerfeld
Abstract: Using the properties of the local Boltzmann weights of integrable interaction-round-a-face (IRF or face) models we express local operators in terms of generalized transfer matrices. This allows for the derivation of discrete functional equations for the reduced density matrices in inhomogeneous generalizations of these models. We apply these equations to study the density matrices for IRF models of various solid-on-solid type and quantum chains of non-Abelian \({su(2)_3}\) or Fibonacci anyons. Similar as in the six vertex model we find that reduced density matrices for a sequence of consecutive sites can be 'factorized', i.e. expressed in terms of nearest-neighbour correlators with coefficients which are independent of the model parameters. Explicit expressions are provided for correlation functions on up to three neighbouring sites.
Organisation(s): Institute of Theoretical Physics
Type: Article
Journal: SciPost Physics
Volume: 11
No. of pages: 40
Publication date: 14.09.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Physics and Astronomy(all)
Electronic version(s): https://arxiv.org/abs/2104.06269 (Access: Open)
https://doi.org/10.21468/SciPostPhys.11.3.057 (Access: Open)

BibTeX

@article{5b619fc2004d4b53ba7772b60736b59b,
title = "Density matrices in integrable face models",
abstract = "Using the properties of the local Boltzmann weights of integrable interaction-round-a-face (IRF or face) models we express local operators in terms of generalized transfer matrices. This allows for the derivation of discrete functional equations for the reduced density matrices in inhomogeneous generalizations of these models. We apply these equations to study the density matrices for IRF models of various solid-on-solid type and quantum chains of non-Abelian \({su(2)_3}\) or Fibonacci anyons. Similar as in the six vertex model we find that reduced density matrices for a sequence of consecutive sites can be 'factorized', i.e. expressed in terms of nearest-neighbour correlators with coefficients which are independent of the model parameters. Explicit expressions are provided for correlation functions on up to three neighbouring sites. ",
keywords = "cond-mat.stat-mech, hep-th, math-ph",
author = "Holger Frahm and Daniel Westerfeld",
note = "Funding Information: We would like to thank H. Boos, F. G{\"o}hmann, and A. Kl{\"u}mper for stimulating discussions. This work is part of the programme of the research unit Correlations in Integrable Quantum Many-Body Systems (FOR 2316). Partial Funding has been provided by the Deutsche Forschungsge-meinschaft under grant no. FR 737/8.",
year = "2021",
month = sep,
day = "14",
doi = "10.21468/SciPostPhys.11.3.057",
language = "English",
volume = "11",
journal = "SciPost Physics",
issn = "2542-4653",
publisher = "SciPost Foundation",
number = "3",
}