AI 中文总结
该研究提出哈密顿量的动力学分裂结构，将其应用于手征XYZ模型，通过精确对角化发现其无隙节点玻色态，并揭示其相变至Z₂×Z₂拓扑序有隙相的特性。
AI 中文摘要
我们研究一类具有被称为“动力学分裂”结构的哈密顿量：哈密顿量项可分为作用于同一自由度的两组，其中一组的每一项均与另一组的每一项对易，而组内项并非全部对易。该结构产生了有效自由度的代数对偶性，哈密顿量的两部分在互不重叠的自由度上作用，使得可对自旋数约为常规可及规模两倍的晶格进行精确对角化。我们将其应用于“手征XYZ模型”，这是一种几何阻挫的自旋-1/2模型，定义在三角晶格上，此前作为Majorana-Hubbard模型的特殊极限被提出。该模型还具有反对易的不可缩线对称性，其在局域不可区分态之间施加了依赖于拓扑的精确简并。我们首先研究了其$\boldsymbol{\text{Z}_N}$时钟推广模型，发现大$N$极限下存在具有三条子系统对称性保护节点线的无隙基态。利用动力学分裂和子系统对称性，我们对$N=2$的模型在最大$9\times9$自旋的晶格上进行了精确对角化。多体能隙和二分纠缠提供了与大$N$节点结构一致的无隙态的有力证据：纠缠随$L\boldsymbol{\text{log}}L$标度，并在圆柱上表现出类1+1维共形场论（CFT）的弦标度。最后，我们研究了不稳定性和邻近相，特别地，我们发现证据表明，保持子系统对称性的形变会驱动有限耦合相变，进入具有$\boldsymbol{\text{Z}_2}\times\boldsymbol{\text{Z}_2}$拓扑序的有隙相。
英文摘要
We study a class of Hamiltonians with a structure that we call "dynamical splitting": the Hamiltonian terms can be divided into two sets acting on the same degrees of freedom such that every term in one set commutes with every term in the other, although terms within either set do not all commute. This structure yields an algebraic duality to effective degrees of freedom on which the two parts of the Hamiltonian act disjointly, enabling exact diagonalization on lattices with approximately twice as many spins as usually accessible. We exploit it in the "chiral XYZ model", a geometrically frustrated spin-$1/2$ model on the triangular lattice which was previously introduced as a special limit of a Majorana-Hubbard model. This model also possesses anticommuting noncontractible line symmetries, which enforce an exact, topology-dependent degeneracy between locally indistinguishable states. We first study a $\mathbb{Z}_N$ clock generalization and find, at large $N$, a gapless ground state with three subsystem-symmetry-protected nodal lines. Exploiting dynamical splitting and the subsystem symmetries, we carry out exact diagonalization of the $N=2$ model on lattices up to $9\times9$ spins. The many-body gap and bipartite entanglement provide strong evidence for a gapless state consistent with the large-$N$ nodal structure: the entanglement scales as $L\log L$ and exhibits $1+1$-dimensional CFT-like chord scaling on cylinders. Finally, we study instabilities and proximate phases. In particular, we find evidence that a subsystem-symmetry-preserving deformation drives a finite coupling transition to a gapped phase with $\mathbb Z_2 \times \mathbb Z_2$ topological order.
Comments20 pages + Appendices, 8 figures
