Kitaev蜂窝模型的物理解
Physical solutions of the Kitaev honeycomb model
摘要：
我们研究了Kitaev提出的蜂窝模型的精确解，并导出了投影到物理子空间上的显式公式。这些物理态的简单特征是费米子本征模总占据的宇称。我们考虑一个一般的格子上的环面和物理费米子宇称依赖于在一个非平凡的方式上的涡旋配置和边界条件的选择。在无涡旋的情况下，在一个恒定的规范场，我们能够得到一个解析表达式的宇称。对于一般的规范场组态，宇称可以很容易地用数值计算，这使得大自旋模型可以精确对角化。我们认为物理相关的量，特别是涡旋能量，并表明，它们的真实值和相关的状态可以是从一个在未投影的空间计算，即使在热力学极限有很大的不同。
英文摘要：
We investigate the exact solution of the honeycomb model proposed by Kitaev and derive an explicit formula for the projector onto the physical subspace. The physical states are simply characterized by the parity of the total occupation of the fermionic eigenmodes. We consider a general lattice on a torus and show that the physical fermion parity depends in a nontrivial way on the vortex configuration and the choice of boundary conditions. In the vortex-free case with a constant gauge field we are able to obtain an analytical expression of the parity. For a general configuration of the gauge field the parity can be easily evaluated numerically, which allows the exact diagonalization of large spin models. We consider physically relevant quantities, as in particular the vortex energies, and show that their true value and associated states can be substantially different from the one calculated in the unprojected space, even in the thermodynamic limit.
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