横场中Toric码模型的自对偶性和束缚态
Self-duality and bound states of the toric code model in a transverse field
摘要：
我们研究了横向磁场对复曲面编码模型的影响。我们表明，这个问题可以映射到徐摩尔模型，从而到量子罗盘模型，这是已知的自对偶。我们通过微扰连续么正变换分析低能谱，准确地确定了各个对称扇形的能隙。我们的结果是在非常好的协议与精确的对角化数据的所有值的参数，除了在自对偶点的水平交叉是负责一个拓扑相位和极化相位之间的一阶相变。有趣的是，两个和四个准粒子的费米和玻色子统计的束缚态出现，并显示减少维数的色散关系。
英文摘要：
We investigate the effect of a transverse magnetic field on the toric code model. We show that this problem can be mapped onto the Xu-Moore model and thus onto the quantum compass model which are known to be self-dual. We analyze the low-energy spectrum by means of perturbative continuous unitary transformations and determine accurately the energy gaps of various symmetry sectors. Our results are in very good agreement with exact diagonalization data for all values of the parameters except at the self-dual point where level crossings are responsible for a first order phase transition between a topological phase and a polarized phase. Interestingly, bound states of two and four quasiparticles with fermionic and bosonic statistics emerge, and display dispersion relations of reduced dimensionality.
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