Ground state of antiferromagnetic Heisenberg two-leg ladder in terms of the valence-bond solid picture

TL;DR

This paper introduces the plaquette-singlet solid (PSS) state as a new description of the ground state for spin-1 antiferromagnetic Heisenberg two-leg ladders, linking it to valence-bond solid (VBS) states and exploring phase transitions.

Contribution

It proposes the PSS ground state for the spin-1 ladder and establishes its correspondence with VBS states of spin chains, extending the VBS picture to higher spins.

Findings

Identification of quantum phase transitions with bond alternation.

Establishment of the PSS state as a valid ground state description.

Extension of VBS picture applicability to spin-S two-leg ladders.

Abstract

We have proposed the plaquette-singlet solid (PSS) ground state for the spin-1 antiferromagnetic Heisenberg two-leg ladder. Based on the PSS picture, we discuss the correspondence of the PSS state to the valence-bond solid (VBS) state of the ground state of spin-2 chain by introducing an appropriate composite spin picture. When the bond alternation is introduced, there occur quantum phase transitions and each phase can be identified with that in the dimerized spin-2 chain. Furthermore, we argue that the VBS picture of spin-2S chain can be applied to the ground state of spin-S two-leg ladder.