First Order Transitions Between the Gapped Spin-Liquid and Ferrimagnetic Phases in (1/2,1/2,1) Mixed Diamond Chains with Bond Alternation

Abstract

The ground-state phases of mixed diamond chains with bond alternation $\delta$, and ($S,{\tau }^{(1)},{\tau }^{(2)})=(1/2,1/2,1)$, where $S$ is the magnitude of vertex spins, and ${\tau }^{(1)}$ and ${\tau }^{(2)}$ are those of apical spins, are investigated. The two apical spins in each unit cell are connected by an exchange coupling $\lambda$. The exchange couplings between the apical spins and the vertex spins take the values $1+\delta$ and $1-\delta$ alternatingly. This model has an infinite number of local conservation laws. For large $\lambda$ and $\delta \ne 0$, the ground state is equivalent to that of the spin $1/2$ chain with bond alternation. Hence, the ground state is a gapped spin liquid. This energy gap vanishes for $\delta =0$. With the decrease of $\lambda$, the ground state undergoes a transition at $\lambda ={\lambda }_{c0}(\delta )$ to a series of ferrimagnetic phases with a spontaneous magnetization $m_{\mathrm{sp}}=1/p$ per unit cell where $p$ is a positive integer. It is found that this transition is a first order transition for $\delta \ne 0$ with a discontinuous change in $m_{\mathrm{sp}}$, while no discontinuity is found for $\delta =0$. The critical behaviors of $m_{\mathrm{sp}}$ and ${\lambda }_{c0}(\delta )$ around the critical point $(\delta ,\lambda )=(0,{\lambda }_{c0}(\delta ))$ are also discussed analytically.

5 pages, 5 figures. Several mistakes in equations are corrected. Work closely related to arXiv:2102.02116(=J. Phys. Soc. Jpn. 90, 054701 (2021))

References in corpus (4)

• Haldane Phases and Ferrimagnetic Phases with Spontaneous Translational Symmetry Breakdown in Distorted Mixed Diamond Chains with Spins 1 and 1/2
• Ground State Phase Diagram of S=1 Diamond Chains
• Ground State Phases of Distorted $S=1$ Diamond Chains
• Infinite Series of Ferrimagnetic Phases Emergent from the Gapless Spin Liquid Phase of Mixed Diamond Chains