Eigenvectors of open Bazhanov-Stroganov quantum chain

TL;DR

This paper provides an explicit formula for the eigenvectors of the Hamiltonians in the open Bazhanov-Stroganov quantum chain, utilizing an iterative method and special functions related to roots of unity.

Contribution

It introduces a new explicit formula for eigenvectors of the open Bazhanov-Stroganov quantum chain Hamiltonians, derived via an iterative approach and expressed through specialized root of unity functions.

Findings

Explicit eigenvector formulas for the quantum chain Hamiltonians.

Use of $w_p(s)$-function as a root of unity analogue of $ ext{Gamma}_q$-function.

Application of iterative procedures to derive eigenvectors.

Abstract

In this contribution we give an explicit formula for the eigenvectors of Hamiltonians of open Bazhanov-Stroganov quantum chain. The Hamiltonians of this quantum chain is defined by the generation polynomial $A_n(\lambda)$ which is upper-left matrix element of monodromy matrix built from the cyclic $L$-operators. The formulas for the eigenvectors are derived using iterative procedure by Kharchev and Lebedev and given in terms of $w_p(s)$-function which is a root of unity analogue of $\Gamma_q$-function.