一维费米硬棒气体的非对角基态性质
Off-diagonal Ground State Properties of a 1D Gas of Fermi Hard Rods
摘要：
本文用变分Monte Carlo方法计算了费米硬棒系统的单体密度矩阵和动量分布，并与相应的玻色子系统作了比较。由于我们对精确的基态波函数进行了采样，其解析表达式是已知的，因此计算在统计误差范围内是精确的。数值结果与已知的Luttinger液体的渐近展开式吻合得很好。我们发现，玻色子和费米子密度矩阵的绝对值之间的差异变得微不足道的密度增加。在同一区域，相应的动量分布合并成一个独立于统计的共同轮廓。非分析的贡献的一个机构密度矩阵也进行了讨论，并发现是相关的密度增加。
英文摘要：
A variational Monte Carlo calculation of the one-body density matrix and momentum distribution of a system of Fermi hard rods (HR) is presented and compared with the same quantities for its bosonic counterpart. The calculation is exact within statistical errors since we sample the exact ground state wave function, whose analytical expression is known. The numerical results are in good agreement with known asymptotic expansions valid for Luttinger liquids. We find that the difference between the absolute value of the bosonic and fermionic density matrices becomes marginally small as the density increases. In this same regime, the corresponding momentum distributions merge into a common profile that is independent of the statistics. Non-analytical contributions to the one--body density matrix are also discussed and found to be less relevant with increasing density.
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