超对称，格点费米子，独立复形和上同调理论
Supersymmetry, lattice fermions, independence complexes and cohomology theory
摘要：
我们分析了一个特定模型的巡回，强相互作用的晶格费米子的量子基态结构。相互作用被调整以使模型超对称。因此，量子基态与所谓的晶格独立复合体的上同调类一一对应。我们的主要结果是一个完整的描述的上同调，从而量子基态，一个二维正方形晶格周期边界条件。我们的工作建立在J. Jonsson的结果之上，他通过与平面的菱形拼接的对应关系确定了欧拉特征线（威滕指数）。我们证明了一个定理，首先由P.Fendley，它涉及的维数的上同调在等级n的菱形平铺与n个菱形的数量。
英文摘要：
We analyze the quantum ground state structure of a specific model of itinerant, strongly interacting lattice fermions. The interactions are tuned to make the model supersymmetric. Due to this, quantum ground states are in one-to-one correspondence with cohomology classes of the so-called independence complex of the lattice. Our main result is a complete description of the cohomology, and thereby of the quantum ground states, for a two-dimensional square lattice with periodic boundary conditions. Our work builds on results by J. Jonsson, who determined the Euler characteristic (Witten index) via a correspondence with rhombus tilings of the plane. We prove a theorem, first conjectured by P. Fendley, which relates dimensions of the cohomology at grade n to the number of rhombus tilings with n rhombi.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
