强变形托里码的带隙母哈密顿量

中文摘要 AI 辅助

拓扑有序波函数的局域非幺正形变可驱动相变进入挑战现代带隙量子物质视角的奇特态。强变形托里码是一个有趣的案例，其同时具有m任意子凝聚和在精确1-形式对称下带电的威尔逊环的周长定律标度——这些性质通常不会在带隙基态中共存。尽管如此，我们为这些强变形托里码态严格构造了局域带隙母哈密顿量。我们构造的哈密顿量并非严格有限范围，而是包含威尔逊环算子的求和项，其系数随环的直径指数衰减。若采用定义带隙相的标准局域性边界（允许此类指数衰减项），我们的构造表明这些态实现了平凡带隙相。在该局域性类别内，我们证明威尔逊环的周长定律标度并不意味着1-形式对称的自发破缺，且从对偶视角看，长程铁磁序与周长定律无序参数关联可在二维带隙基态中共存。我们通过以热力学极限下可量化为良性的方式放宽Sahay等人[arXiv:2503.01977]近期提出的禁则定理的假设，规避了该定理。更广泛地说，我们的结果强调，需要更强的局域性概念才能在带隙相中禁止这些反直觉性质。

英文摘要

Local non-unitary deformations of topologically ordered wavefunctions can drive transitions into peculiar states that challenge modern perspectives on gapped quantum matter. The strongly deformed toric code offers a curious case, hosting $m$ anyon condensation alongside perimeter-law scaling of Wilson loops charged under an exact 1-form symmetry---properties that typically do not coexist in gapped ground states. Nevertheless, we rigorously construct local gapped parent Hamiltonians for these strongly deformed toric code states. The Hamiltonians we construct are not strictly finite-range, but contain sums of Wilson loop operators whose coefficients decay exponentially in their diameter. If one adopts standard locality bounds used to define gapped phases---which allow for such exponentially decaying terms---our construction shows that these states realize a trivial gapped phase. Within this locality class, we demonstrate that perimeter-law scaling of Wilson loops does not imply a spontaneously broken 1-form symmetry, and from a dual perspective, that long-range ferromagnetic order and perimeter-law disorder parameter correlations can coexist in a 2D gapped ground state. We evade a recent no-go theorem [Sahay et al., arXiv:2503.01977] by relaxing its assumptions in a manner that we quantify as benign in the thermodynamic limit. More broadly, our results highlight that stronger notions of locality are necessary for prohibiting these counterintuitive properties within a gapped phase.

补充信息

备注

7 + 25 pages, 1 + 2 figures