论文标题
通过图形不变的表征可解决的自旋模型
Characterization of solvable spin models via graph invariants
论文作者
论文摘要
确切的可解决模型在物理中至关重要。对于多体Spin-1/2系统，重要类型的模型由可以映射到图形上的费米子的模型组成。我们提供了可以通过这种方式解决的模型的完整表征。具体而言，我们将识别此类自旋模型的问题减少到识别线图的图理论问题，该问题已最佳地求解。我们的结果的必然是一组恒定尺寸的换向结构，构成了自由屈服解决方案的障碍物。我们发现在这些模型中对称性受到严格的约束。 Pauli对称性对应于：（i）fermion跳图上的循环，（ii）fermion parity操作员，或（iii）逻辑编码的量子。这些对称部门之一中的克利福德对称性，除三个例外，必须是自由屈服模型本身的对称性。我们演示了文献中的几种确切的自由屈服解决方案如何适合我们的形式主义，并给出了一个以前未知的新模型的明确示例，该模型无法通过自由费米斯解决。
Exactly solvable models are essential in physics. For many-body spin-1/2 systems, an important class of such models consists of those that can be mapped to free fermions hopping on a graph. We provide a complete characterization of models which can be solved this way. Specifically, we reduce the problem of recognizing such spin models to the graph-theoretic problem of recognizing line graphs, which has been solved optimally. A corollary of our result is a complete set of constant-sized commutation structures that constitute the obstructions to a free-fermion solution. We find that symmetries are tightly constrained in these models. Pauli symmetries correspond to either: (i) cycles on the fermion hopping graph, (ii) the fermion parity operator, or (iii) logically encoded qubits. Clifford symmetries within one of these symmetry sectors, with three exceptions, must be symmetries of the free-fermion model itself. We demonstrate how several exact free-fermion solutions from the literature fit into our formalism and give an explicit example of a new model previously unknown to be solvable by free fermions.
