标题： 关联约化密度矩阵的投影纯化 显示英文标题

标题： Projective purification of correlated reduced density matrices

摘要： 在寻找多体薛定谔方程的精确近似解的过程中，约化密度矩阵起着重要作用，因为它们允许以粒子数的多项式尺度来制定近似方法。然而，这些方法经常遇到$N$-可表示性问题，在方法的自洽应用中，约化密度矩阵变得不物理。过去提出了一些算法，以在约化密度矩阵出现缺陷后恢复给定的$N$-可表示性条件。然而，这些纯化算法要么忽略了与守恒量相关的哈密顿量对称性，要么没有以有效的方式将其纳入，从而比必要程度更大地修改了约化密度矩阵。在本文中，我们提出了一种算法，能够在最少侵入性的方式下高效完成以下所有任务：恢复给定的$N$-可表示性条件，保持约化密度矩阵各阶之间的收缩一致性，并保留所有守恒量。我们在时间依赖的两体约化密度矩阵方法应用于费米-哈伯德模型淬火动力学的背景下，展示了当前纯化算法优于以往算法的优势。 显示英文摘要

摘要： In the search for accurate approximate solutions of the many-body Schr\"odinger equation, reduced density matrices play an important role, as they allow to formulate approximate methods with polynomial scaling in the number of particles. However, these methods frequently encounter the issue of $N$-representability, whereby in self-consistent applications of the methods, the reduced density matrices become unphysical. A number of algorithms have been proposed in the past to restore a given set of $N$-representability conditions once the reduced density matrices become defective. However, these purification algorithms have either ignored symmetries of the Hamiltonian related to conserved quantities, or have not incorporated them in an efficient way, thereby modifying the reduced density matrix to a greater extent than is necessary. In this paper, we present an algorithm capable of efficiently performing all of the following tasks in the least invasive manner: restoring a given set of $N$-representability conditions, maintaining contraction consistency between successive orders of reduced density matrices, and preserving all conserved quantities. We demonstrate the superiority of the present purification algorithm over previous ones in the context of the time-dependent two-particle reduced density matrix method applied to the quench dynamics of the Fermi-Hubbard model.