Ground-state properties of anyons in a one-dimensional lattice
Ground-state properties of anyons in a one-dimensional lattice
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DOI：
10.1088/1367-2630/17/12/123016
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发表时间：
2015-09
影响因子：
3.3
通讯作者：
G. Tang;S. Eggert;A. Pelster
中科院分区：
文献类型：
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作者：
G. Tang;S. Eggert;A. Pelster
利用任意子哈伯德哈密顿量，我们分析了一维晶格中任意子的基态性质。为此，我们映射的相关任意子的跳跃动力学的占用依赖跳跃玻色-哈伯德模型使用分数的乔丹-维格纳变换。特别地，我们计算了任意子的准动量分布，它介于玻色-爱因斯坦和费米-狄拉克统计之间。在分析上，我们应用一个修改后的Gutzwiller平均场方法，它超越了经典的一个，包括分数相位的任意子内的多体波函数的影响。在数值上，我们依靠矩阵乘积状态的拟设来使用密度矩阵重整化群。结果表明，任意子的准动量分布既有峰值漂移又有非对称性，这主要源于弦的非定域性质。此外，我们确定了相应的准动量分布的约旦-维格纳变换玻色子，其中，在对比的硬核的情况下，我们还观察到一个不对称的软核的情况下，这强烈依赖于粒子数密度。
Using the Anyon–Hubbard Hamiltonian, we analyze the ground-state properties of anyons in a one-dimensional lattice. To this end we map the hopping dynamics of correlated anyons to an occupation-dependent hopping Bose–Hubbard model using the fractional Jordan–Wigner transformation. In particular, we calculate the quasi-momentum distribution of anyons, which interpolates between Bose–Einstein and Fermi–Dirac statistics. Analytically, we apply a modified Gutzwiller mean-field approach, which goes beyond a classical one by including the influence of the fractional phase of anyons within the many-body wavefunction. Numerically, we use the density-matrix renormalization group by relying on the ansatz of matrix product states. As a result it turns out that the anyonic quasi-momentum distribution reveals both a peak-shift and an asymmetry which mainly originates from the nonlocal string property. In addition, we determine the corresponding quasi-momentum distribution of the Jordan–Wigner transformed bosons, where, in contrast to the hard-core case, we also observe an asymmetry for the soft-core case, which strongly depends on the particle number density.