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arXiv 1005.4929cond-mat.supr-concond-mat.quant-gascond-mat.str-el
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硬核玻色子的涡旋动力学和Hall电导

Vortex Dynamics and Hall Conductivity of Hard Core Bosons

Netanel H. Lindner, Assa Auerbach, Daniel P. Arovas

摘要:

采用XXZ量子自旋模型表象研究了硬核玻色子的磁输运,在环面上进行适当的规范以考虑外部磁场。我们发现强晶格效应接近半填充。一个有效的量子力学描述的涡旋自由度。利用半经典和数值分析,我们计算了涡旋跳跃能量,在半填充接近玻色子跳跃能量的大小。涡旋晶格的临界量子熔化密度估计为6.5 × 10 -5个涡旋/晶胞。霍尔电导由低能本征态的陈数计算。在零温度下,它在半填充时突然反转符号。在精确的半填充,所有的本征态是双简并的任何奇数通量量子。通过构造一个与涡度中心相关的点群对称SU(2)代数,我们证明了环面上的精确退化。这一结果被解释为,如果每个漩涡进行内部自旋半自由度(“vspin”),这可以表现为在其核心的电荷密度调制本身。我们的发现对光晶格中冷原子的涡旋运动和短相干长度超导体的磁输运具有重要的实验意义。

英文摘要:

Magneto-transport of hard core bosons (HCB) is studied using an XXZ quantum spin model representation, appropriately gauged on the torus to allow for an external magnetic field. We find strong lattice effects near half filling. An effective quantum mechanical description of the vortex degrees of freedom is derived. Using semiclassical and numerical analysis we compute the vortex hopping energy, which at half filling is close to magnitude of the boson hopping energy. The critical quantum melting density of the vortex lattice is estimated at 6.5x10-5 vortices per unit cell. The Hall conductance is computed from the Chern numbers of the low energy eigenstates. At zero temperature, it reverses sign abruptly at half filling. At precisely half filling, all eigenstates are doubly degenerate for any odd number of flux quanta. We prove the exact degeneracies on the torus by constructing an SU(2) algebra of point-group symmetries, associated with the center of vorticity. This result is interpreted as if each vortex carries an internal spin-half degree of freedom ('vspin'), which can manifest itself as a charge density modulation in its core. Our findings suggest interesting experimental implications for vortex motion of cold atoms in optical lattices, and magnet-transport of short coherence length superconductors.

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