发表机构
University of Colorado, Boulder; Caltech; Institute for Advanced Study; Massachusetts Institute of Technology; University of Chicago; University of California, Los Angeles（科罗拉多大学博尔德分校; 加州理工学院; 普林斯顿高等研究院; 麻省理工学院; 芝加哥大学; 加州大学洛杉矶分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究整数谱对易投影子哈密顿量（如伊辛铁磁体和环面码）能否在辅助系统下实现局域对称性，证明有限维辅助下不可能，而无限维辅助下可解缠并实现局域对称性。
AI 中文摘要
具有整数谱的对易投影子哈密顿量，例如1+1维伊辛铁磁体和2+1维环面码，可以被视为非局域$U(1)$对称性的生成元。在本文中，我们研究了在有限维和无限维辅助系统存在的情况下，这些对称性是否可以被实现为局域对称性。在有限维情形下，我们证明了分数化激发，如畴壁和任意子，使得这些哈密顿量无法被局域化。另一方面，我们表明当允许无限维辅助系统（例如转子）时，1+1维伊辛铁磁体和2+1维环面码都可以被解缠，从而产生局域对称性。这并不与这些哈密顿量的非平凡基态序相矛盾，因为辅助哈密顿量不再有下界。我们的结果表明，在存在无限维辅助系统的情况下，格点和量子场论异常之间存在一致性，而在有限维辅助系统下，局域化的障碍甚至可能是不可逆的。
英文摘要
Commuting-projector Hamiltonians with integer spectrum such as the 1+1d Ising ferromagnet and the 2+1d toric code may be regarded as the generators of non-on-site $U(1)$ symmetries. In this paper we study whether these symmetries can be made on-site in the presence of finite and infinite-dimensional ancillae. In the finite-dimensional case, we prove that the fractionalized excitations, such as domain walls and anyons, make it impossible to on-site these Hamiltonians. On the other hand, we show that when infinite dimensional ancillae (e.g., rotors) are allowed, both the 1+1d Ising ferromagnet and the 2+1d toric code can be disentangled, yielding on-site symmetries. This is not in contradiction with the non-trivial ground state order of these Hamiltonians, since the ancilla Hamiltonians are no longer bounded from below. Our results indicate agreement between lattice and quantum field theory anomalies in the presence of infinite-dimensional ancillae, while with finite-dimensional ancillae the obstruction to on-siteability may even be non-invertible.
Comments14+9 pages, 4 figures
