Infinite Series of Ferrimagnetic Phases Emergent from the Gapless Spin Liquid Phase of Mixed Diamond Chains

Abstract

The ground-state phases of mixed diamond chains with ($S, τ^{(1)}, τ^{(2)})=(1/2,1/2,1)$, where $S$ is the magnitude of vertex spins, and $τ^{(1)}$ and $τ^{(2)}$ are those of apical spins, are investigated. The apical spins $τ^{(1)}$ and $τ^{(2)}$ are connected with each other by an exchange coupling $λ$. Other exchange couplings are set equal to unity. This model has an infinite number of local conservation laws. For large $λ$, the ground state is equivalent to that of the uniform spin $1/2$ chain. Hence, the ground state is a gapless spin liquid. For $λ\leq 0$, the ground state is a Lieb-Mattis ferrimagnetic phase with spontaneous magnetization $m_{\rm sp}=1$ per unit cell. For intermediate $λ$, we find a series of ferrimagnetic phases with $m_{\rm sp}=1/p$ where $p$ takes positive integer values. The phases with $p \geq 2$ are accompanied by the spontaneous breakdown of the $p$-fold translational symmetry. It is suggested that the phase with arbitrarily large $p$, namely infinitesimal spontaneous magnetization, is allowed as $λ$ approaches the transition point to the gapless spin liquid phase.