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

TL;DR

This paper explores the complex phase diagram of mixed diamond chains, revealing an infinite series of ferrimagnetic phases emerging from a gapless spin liquid state, with novel spontaneous symmetry breaking phenomena.

Contribution

It introduces a detailed analysis of ferrimagnetic phases with fractional magnetization in a model with local conservation laws, highlighting an infinite series of such phases near a spin liquid.

Findings

Infinite series of ferrimagnetic phases with fractional magnetization.

Spontaneous breakdown of translational symmetry in these phases.

Existence of a phase with infinitesimal spontaneous magnetization near the transition.

Abstract

The ground-state phases of mixed diamond chains with ($S, \tau^{(1)}, \tau^{(2)})=(1/2,1/2,1)$, where $S$ is the magnitude of vertex spins, and $\tau^{(1)}$ and $\tau^{(2)}$ are those of apical spins, are investigated. The apical spins $\tau^{(1)}$ and $\tau^{(2)}$ are connected with each other by an exchange coupling $\lambda$. Other exchange couplings are set equal to unity. This model has an infinite number of local conservation laws. For large $\lambda$, the ground state is equivalent to that of the uniform spin $1/2$ chain. Hence, the ground state is a gapless spin liquid. For $\lambda \leq 0$, the ground state is a Lieb-Mattis ferrimagnetic phase with spontaneous magnetization $m_{\rm sp}=1$ per unit cell. For intermediate $\lambda$, 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 $\lambda$ approaches the transition point to the gapless spin liquid phase.