Quantum walks of two interacting anyons in one-dimensional optical lattices
Quantum walks of two interacting anyons in one-dimensional optical lattices
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一维光学晶格中两个相互作用的任意子的量子行走
DOI：
10.1103/physreva.90.063618
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发表时间：
2014-11
影响因子：
2.9
通讯作者：
Yunbo Zhang
中科院分区：
文献类型：
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作者：
Limin Wang;Li Wang;Yunbo Zhang
基于分数Jordan-Wigner变换，研究了一维晶格中两个不可分辨任意子在原位和最近邻相互作用下的连续时间量子行走。结果表明，在位置空间中，两体关联在玻色极限（$\chi=0$）和费米极限（$\chi=1$）下关于两个量子步行者的初始位置是对称的，而在动量空间中，这只发生在玻色极限下.一个有趣的不对称性出现在大多数情况下的相关性与统计参数$\chi$之间的变化。事实证明，这种不对称性的起源来自任意子服从的分数统计。另一方面，硬核任意子在位置空间中的两体关联表现出从反聚束到共步的一致行为，而与统计参数无关。在强相互作用情况下，动量关联经历了两条平滑合并为一条的平滑过程，即费米子向硬核玻色子的演化。
We investigate continuous-time quantum walks of two indistinguishable anyons in one-dimensional lattices with both on-site and nearest-neighbor interactions based on the fractional Jordan-Wigner transformation. It is shown that the two-body correlations in position space are symmetric about the initial sites of two quantum walkers in the Bose limit ($\chi=0$ ) and Fermi limit ( $\chi=1$), while in momentum space this happens only in the Bose limit. An interesting asymmetry arises in the correlation for most cases with the statistical parameter $\chi$ varying in between. It turns out that the origin of this asymmetry comes from the fractional statistics that anyons obey. On the other hand, the two-body correlations of hard-core anyons in position spaceshow uniform behaviors from anti-bunching to co-walking regardless of the statistical parameter. The momentum correlations in the case of strong interaction undergo a smooth process of two stripes smoothly merging into a single one, i.e. the evolution of fermions into hard-core bosons.
DOI：
10.1142/0961
发表时间：
1990-10
期刊：
--
影响因子：
--
作者：
F. Wilczek;D. Rokhsar
通讯作者：
F. Wilczek;D. Rokhsar