AI 中文总结
该研究提出阻挫磁体中精确局域手征约束的SU(2)不变哈密顿量，发现不同连接方式下的集体零模式行为，建立了手征性、约束几何与量子简并性关联的可处理框架。
AI 中文摘要
局域约束支配阻挫物质的低能物理，但常见的冰型规则仅约束类通量量，且对於手征性不敏感。本文证明手征性本身可作为精确的局域量子约束，且无需在自旋空间中选定某一轴。我们构造了半正定、SU(2)不变的母哈密顿量，其在四面体上的完整零能空间具有规定的手征符号，而非选定特定手征波函数。对于自旋1/2，局域项是投影到手征单重态的秩一算子；对于任意自旋，其通过单重态湮灭算子分解为$B^\top B$，其完全表征的核由全局旋转后的手征色冰态的张成给出。对于相干态，同一零能条件成为与$S$无关的非线性约束，其中三个自旋方向通过默比乌斯变换确定第四个；这些映射的组合定义了扩展晶格上的约束完整群。以不同方式连接相同的局域约束会产生定性不同的集体 regime：角共享晶格保留指数级大的量子基态核，其严格下界超过常规冰基准；边共享晶格支持亚维度平面或线零模式；而三角结构抑制非均匀相干变形，且在恰好零能处包含完整的安德森四面体磁序塔。两种不等价的三角覆盖进一步表明，谐波零模式计数无法确定量子核的大小。这些结果建立了一个可处理的框架，其中局域手征性、非线性约束几何与量子简并性可被解耦，并直接与约束网络的连通性相关联。
英文摘要
Local constraints govern the low-energy physics of frustrated matter, but familiar ice-type rules constrain flux-like quantities and are insensitive to handedness. Here we show that handedness itself can be imposed as an exact local quantum constraint without selecting an axis in spin space. We construct positive-semidefinite, SU(2)-invariant parent Hamiltonians whose complete zero-energy space on a tetrahedron has a prescribed chirality sign, rather than selecting a particular chiral wave function. For spin-1/2 the local term is a rank-one projector onto a chiral tetrahedral singlet, while for arbitrary spin it factorizes as $B^\dagger B$ through a singlet-annihilation operator, with a completely characterized kernel given by the span of the globally rotated chiral color-ice states. For coherent states, the same zero-energy condition becomes an $S$-independent nonlinear constraint in which three spin directions determine the fourth through a Möbius transformation; compositions of these maps define constraint holonomies on extended lattices. Connecting the same local constraint in different ways produces qualitatively different collective regimes: corner-sharing lattices retain exponentially large quantum ground-state kernels, with rigorous lower bounds exceeding conventional ice benchmarks; edge-sharing lattices support subdimensional plane or line zero modes; while triangular constructions suppress nonuniform coherent deformations and contain the complete Anderson tower of tetrahedral magnetic order at exactly zero energy. Two inequivalent triangular coverings further show that harmonic zero-mode counting does not determine the size of the quantum kernel. These results establish a tractable setting in which local handedness, nonlinear constraint geometry, and quantum degeneracy can be disentangled and related directly to the connectivity of the constraint network.
Comments50 pages, 13 figures, 10 tables
