无自旋费米子紧束缚模型的阿贝尔Chern-Simons-Maxwell理论
Abelian Chern-Simons-Maxwell theory from a tight binding model of spinless fermions
摘要：
阿贝尔陈-西蒙斯-麦克斯韦理论可以从描述相互作用狄拉克费米子的2+1维瑟灵模型的玻色化中产生。在这里，我们展示了Thirring模型如何在无自旋费米子的二维紧束缚模型的低能极限中表现出来。为了证明这一点，我们采用了Halfton模型的一个修正，其中费米子的“加倍”是通过绝热消除来纠正的。随后，费米子相互作用的引入，导致易于分析的Thirring模型。通过对晶格费米子的局域密度测量，我们可以确定，对于特定的耦合值，模型表现出2+1维QED相或拓扑有序相，对应于Chern-Simons理论。该模型的实现以及测量协议与当前光晶格中冷原子的技术是可访问的。
英文摘要：
Abelian Chern-Simons-Maxwell theory can emerge from the bosonisation of the 2+1-dimensional Thirring model that describes interacting Dirac fermions. Here we show how the Thirring model manifests itself in the low energy limit of a two-dimensional tight-binding model of spinless fermions. To establish that we employ a modification of Haldane's model, where the "doubling" of fermions is rectified by adiabatic elimination. Subsequently, fermionic interactions are introduced that lead to the analytically tractable Thirring model. By local density measurements of the lattice fermions we can establish that for specific values of the couplings the model exhibits the confining 2+1-dimensional QED phase or a topological ordered phase that corresponds to the Chern-Simons theory. The implementation of the model as well as the measurement protocol are accessible with current technology of cold atoms in optical lattices.
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