We introduce a variational state for one-dimensional two-orbital Hubbard models that intuitively explains the recent computational discovery of pairing in these systems when hole doped. Our ansatz is an optimized linear superposition of Affleck–Kennedy–Lieb–Tasaki valence-bond states, rendering the combination a valence-bond liquid dubbed orbital resonant valence bond. We show that the undoped (one-electron/orbital) quantum state of two sites coupled into a global spin singlet is exactly written employing only spin-1/2 singlets linking orbitals at nearest-neighbor sites. Generalizing to longer chains defines our variational state visualized geometrically expressing our chain as a two-leg ladder, with one orbital per leg. As in Anderson’s resonating valence-bond state, our undoped variational state contains preformed singlet pairs that via doping become mobile, leading to superconductivity. Doped real materials with one-dimensional substructures, two near-degenerate orbitals, and intermediate Hubbard U/W strengths—W the carrier’s bandwidth—could realize spin-singlet pairing if on-site anisotropies are small. If these anisotropies are robust, spin-triplet pairing emerges.

我们为一维两轨道Hubbard模型引入了一种变分状态，它直观地解释了当掺杂空穴时这些系统中配对的最新计算发现。我们的ansatz是Affleck-Kennedy-Lieb-Tasaki价键态的优化线性叠加，使该组合成为价键液体，配成轨道共振价键。我们显示耦合到全局自旋单峰的两个位点的未掺杂（单电子/轨道）量子态仅使用自旋1/2单峰态连接最近邻位点的轨道来精确地编写。推广到更长的链条定义了我们的变化状态，以几何方式将我们的链条表示为两条腿的梯子，每条腿有一个轨道。就像在安德森的共价键状态一样，我们未掺杂的变化态包含预先形成的单线态对，这些线对通过掺杂变为可移动的，从而导致超导。具有一维子结构，两个近简轨道和中间哈伯德的掺杂真实材料如果现场的各向异性较小，则U / W强度（载波的带宽W）可以实现自旋-单重配对。如果这些各向异性很强，则会出现自旋三重态对。