Exotic Ground State Phases of $S=1/2$ Heisenberg $\Delta$-Chain with Ferromagnetic Main Chain

TL;DR

This study explores the diverse ground state phases of a frustrated spin-1/2 Heisenberg Δ-chain with a ferromagnetic main chain, revealing nonmagnetic phases, spin quadrupolar states, and potential phase transitions.

Contribution

It introduces a comprehensive analysis of the ground states of the Δ-chain model, including the identification of novel nonmagnetic phases and the connection to spin-1 bilinear-biquadratic chains.

Findings

Identification of nonmagnetic ground states

Realization of spin quadrupolar phase in strong coupling regime

Evidence of phase transitions among nonmagnetic phases

Abstract

The ground state phase diagram of the spin-1/2 Heisenberg frustrated $\Delta$-chain with a ferromagnetic main chain is investigated. In addition to the ferromagnetic phase, various nonmagnetic ground states are found. If the ferromagnetic coupling between apical spins and the main chain is strong, this model is approximated by a spin-1 bilinear-biquadratic chain and the spin quadrupolar phase with spin-2 gapless excitation is realized in addition to the Haldane and ferromagnetic phases. In the regime where the coupling between the apical spins and the main chain is weak, the numerical results which suggest the possibility of a series of phase transitions among different nonmagnetic phases are obtained. Physical pictures of these phases are discussed based on the numerical results.