Exact ground states for a class of one-dimensional frustrated quantum spin models

TL;DR

This paper derives exact ground states for two one-dimensional frustrated quantum spin-1/2 models, revealing detailed quantum states and correlations, advancing understanding of quantum phase transitions and spin ladder systems.

Contribution

It provides the first exact solutions for these frustrated models, including their wave functions and correlation properties, using novel recurrence techniques.

Findings

Exact ground state wave functions derived

Models exhibit distinct quantum phases and energy gaps

Recurrence methods enable expectation value calculations

Abstract

We have found the exact ground state for two frustrated quantum spin-1/2 models on a linear chain. The first model describes ferromagnet- antiferromagnet transition point. The singlet state at this point has double-spiral ordering. The second model is equivalent to special case of the spin-1/2 ladder. It has non-degenerate singlet ground state with exponentially decaying spin correlations and there is an energy gap. The exact ground state wave function of these models is presented in a special recurrent form and recurrence technics of expectation value calculations is developed.