Physical solutions of the Kitaev honeycomb model
Physical solutions of the Kitaev honeycomb model
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Kitaev 蜂窝模型的物理解
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
D. Loss
中科院分区：
文献类型：
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作者：
F. Pedrocchi;S. Chesi;D. Loss
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的显式公式。物理状态简单地由费米子本征模的总占据的奇偶性来表征。我们考虑环面上的一般晶格，并表明物理费米子宇称在很大程度上取决于涡旋配置和边界条件的选择。在具有恒定规范场的无涡流情况下，我们能够获得宇称的解析表达式。对于规范场的一般配置，奇偶校验可以很容易地进行数值计算，这允许大自旋模型的精确对角化。我们考虑物理相关量，特别是涡旋能量，并表明它们的真实值和相关状态可能与在未投影空间中计算的值有很大不同，即使在热力学极限下也是如此。
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.