Frantsuzov Pavel A, Mandelshtam Vladimir A
Chemistry Department, University of California at Irvine, Irvine, California 92697, USA.
J Chem Phys. 2004 Nov 15;121(19):9247-56. doi: 10.1063/1.1804495.
The variational Gaussian wave-packet method for computation of equilibrium density matrices of quantum many-body systems is further developed. The density matrix is expressed in terms of Gaussian resolution, in which each Gaussian is propagated independently in imaginary time beta=(k(B)T)(-1) starting at the classical limit beta=0. For an N-particle system a Gaussian exp[(r-q)(T)G(r-q)+gamma] is represented by its center qinR(3N), the width matrix GinR(3Nx3N), and the scale gammainR, all treated as dynamical variables. Evaluation of observables is done by Monte Carlo sampling of the initial Gaussian positions. As demonstrated previously at not-very-low temperatures the method is surprisingly accurate for a range of model systems including the case of double-well potential. Ideally, a single Gaussian propagation requires numerical effort comparable to the propagation of a single classical trajectory for a system with 9(N(2)+N)/2 degrees of freedom. Furthermore, an approximation based on a direct product of single-particle Gaussians, rather than a fully coupled Gaussian, reduces the number of dynamical variables to 9N. The success of the methodology depends on whether various Gaussian integrals needed for calculation of, e.g., the potential matrix elements or pair correlation functions could be evaluated efficiently. We present techniques to accomplish these goals and apply the method to compute the heat capacity and radial pair correlation function of Ne(13) Lennard-Jones cluster. Our results agree very well with the available path-integral Monte Carlo calculations.
用于计算量子多体系统平衡密度矩阵的变分高斯波包方法得到了进一步发展。密度矩阵通过高斯分解来表示，其中每个高斯在虚时间β=(k(B)T)(-1)下从经典极限β=0开始独立传播。对于一个N粒子系统，高斯exp[(r - q)(T)G(r - q)+γ]由其中心qinR(3N)、宽度矩阵GinR(3Nx3N)和尺度γinR表示，所有这些都被视为动态变量。可观测量的评估通过对初始高斯位置的蒙特卡罗采样来完成。如之前在不是非常低的温度下所证明的，该方法对于一系列模型系统（包括双阱势的情况）出奇地准确。理想情况下，对于一个具有9(N(2)+N)/2自由度的系统，单个高斯传播所需的数值工作量与单个经典轨迹的传播相当。此外，基于单粒子高斯的直积而不是完全耦合高斯的近似将动态变量的数量减少到9N。该方法的成功取决于例如计算势矩阵元素或对关联函数所需的各种高斯积分是否能够有效地进行评估。我们提出了实现这些目标的技术，并将该方法应用于计算Ne(13) Lennard-Jones团簇的热容和径向对关联函数。我们的结果与现有的路径积分蒙特卡罗计算非常吻合。
