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- W2891365082 abstract "The scaling of the largest eigenvalue ${ensuremath{lambda}}_{0}$ of the one-body density matrix of a system with respect to its particle number $N$ defines an exponent $mathcal{C}$ and a coefficient $mathcal{B}$ via the asymptotic relation ${ensuremath{lambda}}_{0}ensuremath{sim}mathcal{B}phantom{rule{0.16em}{0ex}}{N}^{mathcal{C}}$. The case $mathcal{C}=1$ corresponds to off-diagonal long-range order. For a one-dimensional homogeneous Tonks-Girardeau gas, a well-known result also confirmed by bosonization gives instead $mathcal{C}=1/2$. Here we investigate the inhomogeneous case, initially addressing the behavior of $mathcal{C}$ in the presence of a general external trapping potential $V$. We argue that the value $mathcal{C}=1/2$ characterizes the hard-core system independently of the nature of the potential $V$. We then define the exponents $ensuremath{gamma}$ and $ensuremath{beta}$, which describe the scaling of the peak of the momentum distribution with $N$ and the natural orbital corresponding to ${ensuremath{lambda}}_{0}$, respectively, and we derive the scaling relation $ensuremath{gamma}+2ensuremath{beta}=mathcal{C}$. Taking as a specific case the power-law potential $V(x)ensuremath{propto}{x}^{2n}$, we give analytical formulas for $ensuremath{gamma}$ and $ensuremath{beta}$ as functions of $n$. Analytical predictions for the coefficient $mathcal{B}$ are also obtained. These formulas are derived by exploiting a recent field theoretical formulation and checked against numerical results. The agreement is excellent." @default.
- W2891365082 created "2018-09-27" @default.
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- W2891365082 date "2018-12-26" @default.
- W2891365082 modified "2023-10-02" @default.
- W2891365082 title "Universal off-diagonal long-range-order behavior for a trapped Tonks-Girardeau gas" @default.
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- W2891365082 doi "https://doi.org/10.1103/physreva.98.063633" @default.
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