论文标题
晶体学相互作用的拓扑阶段和模棱两可的共同体学：假设或不假定
Crystallographic Interacting Topological Phases and Equivariant Cohomology: To assume or not to assume
论文作者
论文摘要
对于符号晶体相互作用的间隙系统，我们在绝热进化下得出了分类。对于非分类基态，此分类是完整的。对于退化案例，我们讨论了一些模棱两可的特征类别给出的一些不变性。我们不假定新兴的相对论领域理论，也不认为阶段形成拓扑谱。我们也不限于具有短距离纠缠的系统，稳定性抵抗微不足道的系统，也不像SPT和设置分类一样假设存在准粒子的存在。使用略有概括的Bloch分解和由基态空间制成的硕士学位，我们表明$ p $ equivariant的共同体学是$ d $维的圆环，会增加不同的相互作用阶段，其中$ p $表示晶体结构的点组。我们将我们的结果与骨晶体晶体学SPT相和A类中的非相互作用的效率晶体学相进行了比较。最后，我们讨论了我们的假设与为晶体学SPT和设定相的假设的关系。
For symmorphic crystalline interacting gapped systems we derive a classification under adiabatic evolution. This classification is complete for non-degenerate ground states. For the degenerate case we discuss some invariants given by equivariant characteristic classes. We do not assume an emergent relativistic field theory nor that phases form a topological spectrum. We also do not restrict to systems with short-range entanglement, stability against stacking with trivial systems nor assume the existence of quasi-particles as is done in SPT and SET classifications respectively. Using a slightly generalized Bloch decomposition and Grassmanians made out of ground state spaces, we show that the $P$-equivariant cohomology of a $d$-dimensional torus gives rise to different interacting phases, where $P$ denotes the point group of the crystalline structure. We compare our results to bosonic symmorphic crystallographic SPT phases and to non-interacting fermionic crystallographic phases in class A. Finally we discuss the relation of our assumptions to those made for crystallographic SPT and SET phases.
