一维分数量子霍尔态中的手征电流
Chiral currents in one-dimensional fractional quantum Hall states
摘要：
我们研究了具有轨道磁通量的玻色子和费米子量子两足梯。在这样的系统中，粒子密度与磁通量的比率$ν$形成相空间，如在量子霍尔效应中。在费米子（玻色子）梯中，当$ν$等于1/奇（偶）整数时，Laughlin分数量子霍尔（Fractional quantum Hall）态对于足够长范围的排斥相互作用是稳定的。作为这些分数态的签名，我们发现一个独特的依赖粒子密度和磁通量的手征电流。这种依赖性的特点是分数填充因子$ν$，并形成了一个严格的测试实现在梯子上，无论是数值模拟或未来的超冷原子实验中的OHH状态。两条腿模型等价于具有自旋-轨道相互作用和塞曼磁场的单个自旋链，因此结果可以直接从一个模型借用到另一个模型。
英文摘要：
We study bosonic and fermionic quantum two-leg ladders with orbital magnetic flux. In such systems, the ratio, $ν$, of particle density to magnetic flux shapes the phase-space, as in quantum Hall effects. In fermionic (bosonic) ladders, when $ν$ equals one over an odd (even) integer, Laughlin fractional quantum Hall (FQH) states are stabilized for sufficiently long ranged repulsive interactions. As a signature of these fractional states, we find a unique dependence of the chiral currents on particle density and on magnetic flux. This dependence is characterized by the fractional filling factor $ν$, and forms a stringent test for the realization of FQH states in ladders, using either numerical simulations or future ultracold-atom experiments. The two-leg model is equivalent to a single spinful chain with spin-orbit interactions and a Zeeman magnetic field, and results can thus be directly borrowed from one model to the other.
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