arXiv 1804.040842018-04-11cond-mat.stat-mechcond-mat.quant-gas

一维量子系统中非对角长程序的偏离

Deviations from Off-Diagonal Long-Range Order in One-Dimensional Quantum Systems

Andrea Colcelli, Giuseppe Mussardo, Andrea Trombettoni

备注：: 8 pages, 4 figures
发表信息：: EuroPhys. Lett. 122, 50006 (2018)
DOI：: 10.1209/0295-5075/122/50006

摘要：

当单体密度矩阵的最大本征值$λ_0$标度为$λ_0 \sim N$时，量子系统表现出非对角长程序（ODLRO），其中$N$是粒子的总数。用$λ_0 \sim N^{\cal C}$定义标度指数${\cal C}$，则${\cal C}=1$对应于ODLRO，${\cal C}=0$对应于密度矩阵轨道的单粒子占据。当使用$0<{\cal C}<1$时，${\cal C}$可用于量化与ODLRO的偏差。本文研究了一维玻色子和任意子量子系统中的指数${\cal C}$。对于$1D$ Lieb-Liniger玻色气体，我们发现，对于小的相互作用，${\cal C}$接近于$1$，这意味着介观凝聚，即在$N$的有限值下（如在$1D$超冷原子的实验中），“凝聚”分数$λ_0/N$的值是可感知的。$1D$任意子提供了在${\cal C}=1$和$0$之间完全插入的可能性。这些系统的${\cal C}$的行为被发现是非单调的耦合常数和统计参数。

英文摘要：

A quantum system exhibits off-diagonal long-range order (ODLRO) when the largest eigenvalue $λ_0$ of the one-body-density matrix scales as $λ_0 \sim N$, where $N$ is the total number of particles. Putting $λ_0 \sim N^{\cal C}$ to define the scaling exponent ${\cal C}$, then ${\cal C}=1$ corresponds to ODLRO and ${\cal C}=0$ to the single-particle occupation of the density matrix orbitals. When $0<{\cal C}<1$, ${\cal C}$ can be used to quantify deviations from ODLRO. In this paper we study the exponent ${\cal C}$ in a variety of one-dimensional bosonic and anyonic quantum systems. For the $1D$ Lieb-Liniger Bose gas we find that for small interactions ${\cal C}$ is close to $1$, implying a mesoscopic condensation, i.e. a value of the "condensate" fraction $λ_0/N$ appreciable at finite values of $N$ (as the ones in experiments with $1D$ ultracold atoms). $1D$ anyons provide the possibility to fully interpolate between ${\cal C}=1$ and $0$. The behaviour of ${\cal C}$ for these systems is found to be non-monotonic both with respect to the coupling constant and the statistical parameter.

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