发表机构
University of Technology Sydney; Phasecraft Ltd.（悉尼科技大学; Phasecraft有限公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过Krylov分解和图论分析，刻画了非通用自由费米子可解模型族，构造Krylov流算符并证明其路径展开与特殊正交代数生成，为寻找精确可解多体哈密顿量提供系统方法。
AI 中文摘要
精确可解模型通常通过其相互作用的结构特征来识别。对于量子自旋哈密顿量，这些特征由反交换泡利项的受挫图（frustration graph）捕捉。受挫图刻画了在耦合强度取任意（即通用）值时映射到自由费米子的广泛自旋模型族。然而，存在非通用可解模型，它们仅在精细调谐的耦合下才允许自由费米子解。在本工作中，我们根据图结构刻画了这样一类模型族。给定Fendley的伪装自由费米子（FFD）链的任意实例，我们构造一组称为Krylov流的算符，这些算符在其有效费米子模式中是精确二次的，从而将其扩展为线性族的自由费米子可解哈密顿量。由于Krylov流在FFD哈密顿量项中是非线性的，该生成族的元素是非通用可解的，因此它们不满足已知的通用可解性条件。我们证明每个Krylov流都允许按受挫图的诱导路径展开，并且它们生成高斯变换的完整特殊正交代数。我们的结果将路径支持识别为非通用可解性的标志，并为寻找精确可解多体哈密顿量提供了系统途径。
英文摘要
Exactly solvable models are often identified from structural features of their interactions. For quantum spin Hamiltonians, these are captured by the frustration graph of anticommuting Pauli terms. The frustration graph characterizes broad families of spin models that map to free fermions for arbitrary, or generic, values of their coupling strengths. Nevertheless, there exist non-generically solvable models that admit free-fermion solutions only at finely tuned couplings. In this work, we characterize a family of such models in terms of graph structures. Given an arbitrary instance of Fendley's free-fermions-in-disguise (FFD) chain, we construct a set of operators, called Krylov currents, that are exactly quadratic in its effective fermionic modes and thus extend it to a linear family of free-fermion solvable Hamiltonians. As the Krylov currents are nonlinear in the FFD Hamiltonian terms, the elements of this generated family are non-generically solvable, and they accordingly fail the known conditions for generic solvability. We prove that every Krylov current admits an expansion in terms of induced paths of the frustration graph and that they generate the full special-orthogonal algebra of Gaussian transformations. Our results identify path support as a signature of non-generic solvability, and they provide a systematic route to finding exactly solvable many-body Hamiltonians.
Comments43 pages, 7 figures
