Highest weight state description of the isotropic spin-1 chain

TL;DR

This paper introduces a new highest weight state basis to exactly analyze the ground and excited states of the isotropic spin-1 chain at specific phase transition points, enhancing computational methods in quantum spin systems.

Contribution

The paper presents an overcomplete highest weight state basis for the spin-1 chain, enabling exact calculations at special phase diagram points.

Findings

Exact ground state expressions at three special points.

Ability to compute excited states and correlation functions.

Enhanced analytical tools for spin-1 chain analysis.

Abstract

We introduce an overcomplete highest weight state basis as a calculational tool for the description of the isotropic spin-1 chain with bilinear exchange coupling J1 and biquadratic coupling J2. The ground state can be expressed exactly at the three special points in the phase diagram where the Hamiltonian corresponds to a sum of nearest neighbor total spin projection operators (J1=0>J2, J1=-J2<0, and J1=-J2/3<0). In particular, at the phase transition point J1=-J2<0 it is possible to exactly compute the ground states, excited states, expectation values, and correlation functions by using the new total spin basis.