This is a historical note. In 1989 we constructed a version of AKLT with unique ground state on a finite graph. Recently the paper became important for description of entanglement in VBS states
A generalized model of Heisenberg quantum antiferromagnet on an arbitrary graph is constructed so that the VBS is the unique ground state. The norm of the base state and equal time multi point correlation functions are computed in terms of generalized hyper geometric functions. For the one-dimensional periodic Heisenberg model we present a method of computing multi point correlation functions based on the study of a commuting family of transfer matrices. The connection of multi point correlators with Young tableaux and Gegenbauer polynomials is found.
Quantum valence bond ice theory for proton-driven quantum spin-dipole liquids
基于最近在$κ$中发现的具有质子涨落的量子自旋液体的实验结果，结合量子质子冰和Anderson的共振价键自旋液体理论，提出了氢键电子系统中的混合量子液体$_3$（QSDL）理论。H-Cat）。在我们的理论中，电子自旋液体和质子偶极液体同时实现在基态称为$\textit{quantum valence bond ice}$。在这种状态下，两者都不能独立于另一个而建立。分析和数值计算表明，该态在自旋和偶极子之间有很大的纠缠熵，远远超过了（粗糙的）Born-Oppenheimer近似。我们还研究了QSDL的稳定性扰动和讨论的影响，实验中的H-猫和它的氘代模拟D-猫。
