Inhomogeneous isotropic quantum spin chain associated with the difference Lamé equation

Abstract

The spectrum and orthogonal eigenbasis are computed of a tridiagonal matrix encoding a finite-dimensional reduction of the difference Lamé equation at the single-gap integral value of the coupling parameter. This entails the exact solution, in terms of single-gap difference Lamé wave functions, for the spectral problem of a corresponding open inhomogeneous isotropic $XY$ chain with coupling constants built from elliptic integers.

Keywords

• 82B23
• 33E10
• 47B36
• 81Q80