## On correlation functions in models related to the Temperley-Lieb algebra

Kohei Fukai, Raphael Kleinemühl, Balázs Pozsgay, Eric Vernier

SciPost Phys. 16, 003 (2024) · published 5 January 2024

- doi: 10.21468/SciPostPhys.16.1.003
- Submissions/Reports

### Abstract

We deal with quantum spin chains whose Hamiltonian arises from a representation of the Temperley-Lieb algebra, and we consider the mean values of those local operators which are generated by the Temperley-Lieb algebra. We present two key conjectures which relate these mean values to existing literature about factorized correlation functions in the XXZ spin chain. The first conjecture states that the finite volume mean values of the current and generalized current operators are given by the same simple formulas as in the case of the XXZ chain. The second conjecture states that the mean values of products of Temperley-Lieb generators can be factorized: they can expressed as sums of products of current mean values, such that the coefficients in the factorization depend neither on the eigenstate in question, nor on the selected representation of the algebra. The coefficients can be extracted from existing work on factorized correlation functions in the XXZ model. The conjectures should hold for all eigenstates that are non-degenerate with respect to the local charges of the models. We consider concrete representations, where we check the conjectures: the so-called golden chain, the $Q$-state Potts model, and the trace representation. We also explain how to derive the generalized current operators from concrete expressions for the local charges.

### Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.-
^{1}Kouhei Fukai, -
^{2}Raphael Kleinemühl, -
^{3}Balázs Pozsgay, -
^{4}Eric Vernier

^{1}Institute for Solid State Physics, University of Tokyo [ISSP]^{2}Bergische Universität Wuppertal / University of Wuppertal [BUW]^{3}Eötvös Loránd Tudományegyetem / Eötvös Loránd University [ELTE]^{4}Laboratoire de Probabilités, Statistique et Modélisation [LPSM]