Inspired by the recent discovery of superconductivity in the nickelate ${\mathrm{Nd}}_{1-x}{\mathrm{Sr}}_x\mathrm{Ni}{\mathrm{O}}_2$, we study a generalized $t\text{−}J$ model to investigate the correlated phases induced by doping spin-1 ${\mathrm{Ni}}^{2+}$ into a spin-$1/2$ Mott insulator formed by ${\mathrm{Ni}}^{1+}$. Based on a three-fermion parton mean-field analysis, we identify a robust fractional Fermi liquid (FL*) phase for almost every doping level. The FL* state is characterized by a small Fermi pocket on top of a spin liquid, which violates the Luttinger theorem of a conventional Fermi liquid and is an example of a symmetric pseudogap metal. Furthermore, we verify our theory in one dimension through density matrix renormalization group simulations on both the generalized $t\text{−}J$ model and a two-orbital Hubbard model. The fractional Fermi liquid reduces to a fractional Luttinger liquid (LL*) in one dimension, which is connected to the conventional Luttinger liquid through a continuous quantum phase transition by tuning interaction strength. Our findings offer insights into correlated electron phenomena in nickelate superconductors and other multiorbital transition-metal oxides with a spin-triplet $d^8$ state.

中文翻译：

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广义t-J模型中的分数费米液体

受到最近发现镍酸盐中超导性的启发 ${钕}_{\mathrm{1个}-X}{r}_X你{\mathrm{Ø}}_{\mathrm{2个}}$，我们研究了广义 $Ť\text{-}Ĵ$ 模型研究掺杂spin-1诱导的相关相 ${你}^{\mathrm{2个}+}$ 旋转$\mathrm{1个}/\mathrm{2个}$ 莫特绝缘子由 ${你}^{\mathrm{1个}+}$。基于三费米子声子平均场分析，我们为几乎每个掺杂水平确定了稳健的分数费米液相（FL *）相。FL *状态的特征是在自旋液体顶部有一个小的费米口袋，这违反了常规费米液体的Luttinger定理，并且是对称伪能隙金属的一个例子。此外，我们通过密度矩阵重归一化组模拟对一维和广义的一维理论进行了验证。$Ť\text{-}Ĵ$模型和两轨道Hubbard模型。费米分数液体在一维还原为分数卢汀液体（LL *），通过调整相互作用强度，通过连续的量子相变将其与常规的卢汀液体连接。我们的发现为自旋三重态的镍酸盐超导体和其他多轨道过渡金属氧化物中的相关电子现象提供了见解。$d^8$ 状态。