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 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 ≤ 0, the ground state is a Lieb–Mattis ferrimagnetic phase with spontaneous magnetization m_sp = 1 per unit cell. For intermediate λ, we find a series of ferrimagnetic phases with m_sp = 1/p where p takes positive integer values. The phases with p ≥ 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.

中文翻译：

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混合金刚石链无间隙自旋液相产生的无穷系列亚铁磁性相

混合金刚石链的基态相与 \（（S，\ tau ^ {（1）}，\ tau ^ {（2）}）=（1 / 2,1 / 2,1）\），其中S是顶点旋转的大小，而τ ^（1）和τ ^（2）是顶点旋转的大小。顶端自旋τ ^（1）和τ ^（2）通过交换耦合λ彼此连接。其他交换联轴器设置为等于1。该模型具有无限数量的本地保护法。对于较大的λ，基态等于均匀自旋1/2链的基态。因此，基态是无间隙的自旋液体。对于λ ≤0时，基态是具有自发磁化一个利布-马提斯铁磁相米_属=每单位像元1。对于中间的λ，我们发现了一系列铁磁相的米_SP = 1 / p，其中p取正整数值。与相位p ≥2伴随的自发击穿p倍平移对称性。建议当λ接近无间隙自旋液相的转变点时，允许具有任意大的p的相，即无限小自发磁化。