论文标题
相互作用的有限温度偏置长距离顺序
Finite Temperature Off-Diagonal Long-Range Order for Interacting Bosons
论文作者
论文摘要
根据Penrose-Obsager-Onsager-Obsager-Obsager-Obsandager标准提供有关单体密度矩阵（$λ_0$）最大特征值（$λ_0$）的总粒子数（$ n $）的表征。设置$λ_0\ sim n^{\ Mathcal {C} _0} $，然后$ \ Mathcal {C} _0 = 1 $对应于ODLRO。中间情况，$ 0 <\ MATHCAL {C} _0 <1 $，将转换不变的系统与（非连接）相关函数的幂律衰减相对应，并且可以看作是识别Quasi-long-Long-long范围顺序。本文的目的是表征以$ \ Mathcal {C} _0 $ [以及相应的数量$ \ Mathcal {C} _ {k \ neq 0} $的相应数量$ \ Mathcal {C} _0 $的odlro属性。我们表明，在热力学限制中，$ \ MATHCAL {C} _ {K \ neq 0} = 0 $。在$ 1D $中，对于非散热温度而言是$ \ Mathcal {C} _0 = 0 $，而在$ 3D $ \ $ \ MATHCAL {C} _0 = 1 $（$ \ Mathcal {C} _0 = 0 $）中，对于比Bose-Iinnstein较小的温度（较大）的（较大）。然后，我们将注意力集中在$ d = 2 $上，研究$ xy $和反派型号以及弱相互作用的玻色气体。 $ \ MATHCAL {C} _0 $的通用值附近的Berezinskii - Kosterlitz-- $ t_ {bkt} $是$ 7/8 $。 $ \ MATHCAL {C} _0 $的依赖性对$ t = 0 $之间的温度（其中$ \ Mathcal {c} _0 = 1 $）和$ t_ {bkt} $在不同的模型中研究了。使用低温膨胀并与蒙特卡洛结果相比，获得了（非扰动）参数$ξ$输入$ 2D $ bose气体状态的方程的估计。我们最终讨论了$ \ Mathcal {C} _0 $的双跳行为，并相应地讨论了异常尺寸$η$，在$ t_ {bkt} $下方的相互作用的限制下。
Characterizing the scaling with the total particle number ($N$) of the largest eigenvalue of the one--body density matrix ($λ_0$), provides informations on the occurrence of the off-diagonal long-range order (ODLRO) according to the Penrose-Onsager criterion. Setting $λ_0\sim N^{\mathcal{C}_0}$, then $\mathcal{C}_0=1$ corresponds to ODLRO. The intermediate case, $0<\mathcal{C}_0<1$, corresponds for translational invariant systems to the power-law decaying of (non-connected) correlation functions and it can be seen as identifying quasi-long-range order. The goal of the present paper is to characterize the ODLRO properties encoded in $\mathcal{C}_0$ [and in the corresponding quantities $\mathcal{C}_{k \neq 0}$ for excited natural orbitals] exhibited by homogeneous interacting bosonic systems at finite temperature for different dimensions. We show that $\mathcal{C}_{k \neq 0}=0$ in the thermodynamic limit. In $1D$ it is $\mathcal{C}_0=0$ for non-vanishing temperature, while in $3D$ $\mathcal{C}_0=1$ ($\mathcal{C}_0=0$) for temperatures smaller (larger) than the Bose-Einstein critical temperature. We then focus our attention to $D=2$, studying the $XY$ and the Villain models, and the weakly interacting Bose gas. The universal value of $\mathcal{C}_0$ near the Berezinskii--Kosterlitz--Thouless temperature $T_{BKT}$ is $7/8$. The dependence of $\mathcal{C}_0$ on temperatures between $T=0$ (at which $\mathcal{C}_0=1$) and $T_{BKT}$ is studied in the different models. An estimate for the (non-perturbative) parameter $ξ$ entering the equation of state of the $2D$ Bose gases, is obtained using low temperature expansions and compared with the Monte Carlo result. We finally discuss a double jump behaviour for $\mathcal{C}_0$, and correspondingly of the anomalous dimension $η$, right below $T_{BKT}$ in the limit of vanishing interactions.
