论文标题
晶格量子小人汉密尔顿人：紧凑型标量，$ u（1）$量表理论，分布型模型和量子iSing模型二重性
Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities
论文作者
论文摘要
我们为紧凑型标量和亚伯仪理论构建了小人汉密尔顿人。小人整数被提升为整体频谱运算符，其规范的结合物自然是紧凑的标量。此外，根据理论，这些共轭运算符可以解释为（高格式）仪表场。如果对这些双量规场施加了尺度对称性，则对反派操作员的自然限制会导致缺陷（例如涡旋，单脚骨，...）。因此，这些晶格模型具有与相应的连续模型相同的对称和异常结构。此外，它们可以以使知识双重性显现的方式进行配制，例如2D中的紧凑型标量具有T偶性，在3D中，对u（1）量规理论等是双重的。我们进一步讨论了晶格上紧凑型标量的测量版，其异常和解决方案，以及在强耦合上的XY XY模型的特定限制，从而将XY模型降低到横向上场模型。高格式理论的结构相似。我们将这些想法应用于某些模型的构造，这些模型对Fracton物理学（尤其是XY-Plaquette模型和张量表字段模型）应用。 2+1D中的XY-Plaquette模型在强量规耦合处与张量规场耦合，也由横向场量子$ j_1-j__2 $ j_1-j_2 $ j_1 = 2j_2 $进行了精确描述，并讨论了此类模型的相结构。
We construct Villain Hamiltonians for compact scalars and abelian gauge theories. The Villain integers are promoted to integral spectrum operators, whose canonical conjugates are naturally compact scalars. Further, depending on the theory, these conjugate operators can be interpreted as (higher-form) gauge fields. If a gauge symmetry is imposed on these dual gauge fields, a natural constraint on the Villain operator leads to the absence of defects (e.g. vortices, monopoles,...). These lattice models therefore have the same symmetry and anomaly structure as their corresponding continuum models. Moreover they can be formulated in a way that makes the well-know dualities look manifest, e.g. a compact scalar in 2d has a T-duality, in 3d is dual to a U(1) gauge theory, etc. We further discuss the gauged version of compact scalars on the lattice, its anomalies and solution, as well as a particular limit of the gauged XY model at strong coupling which reduces to the transverse-field Ising model. The construction for higher-form gauge theories is similar. We apply these ideas to the constructions of some models which are of interest to fracton physics, in particular the XY-plaquette model and the tensor gauge field model. The XY-plaquette model in 2+1d coupled to a tensor gauge fields at strong gauge coupling is also exactly described by a transverse field quantum $J_1-J_2$ Ising model with $J_1=2J_2$, and discuss the phase structure of such models.
