One-dimensional spin pyrochlore lattice: exact ground state and elementary excitations

TL;DR

This paper investigates the ground states and elementary excitations of one-dimensional spin pyrochlore lattices with S=1/2 and S=1, revealing different phases and excitations through analytical and numerical methods.

Contribution

It provides an exact analysis of the ground states and phase diagram of the spin pyrochlore lattice, including new phases and the effects of SU(3) symmetry.

Findings

Strong rung coupling leads to a specific ground state.

Spin-1/2 excitations are gapless, spin-1 have a finite gap.

An intermediate phase with alternating rung singlet and spin states exists.

Abstract

We study the antiferromagnetic spin exchange models with $S=1/2$ and S=1 on a one-dimensional tetrahedron chain by both analytical and numerical approaches. The system is shown to be effectively mapped to a decoupled spin chain in the regime of strong rung coupling, and a spin sawtooth lattice in the regime of weak rung coupling with spin $2S$ on the top row and spin $S$ on the lower row. The ground state for the homogeneous tetrahedron chain is found to fall into in the regime of strong rung coupling. As a result, the elementary excitation for the spin-$ 1/2$ system is gapless whereas the excitation for the spin-1 system has a finite spin gap. With the aid of the exact diagonalization method, we determine the phase diagram numerically and find the existence of an additional phase in the intermediate regime. This phase is doubly degenerate and is characterized by an alternating distribution of rung singlet and rung spin $2S$. We also show that the SU(3) exchange model on the same lattice has completely different kind of ground state from that of its SU(2) correspondence and calculate its ground state and elementary excitation analytically.