论文标题
量子多体问题的变分相关方法
Variational-Correlations Approach to Quantum Many-body Problems
论文作者
论文摘要
我们研究了一种研究量子多体哈密顿量的基态的方法，该方法基于将相关功能视为变异参数。在这种方法中，通过近似逐阶密度矩阵的阳性，以一种跟踪有限的相关函数的方式来估算密度矩阵的阳性，从而规避了指数级的希尔伯特空间所设定的挑战。特别是，密度 - 矩阵描述被一个相关矩阵所取代，其尺寸在系统大小上保持线性的相关矩阵与近似的所有顺序保持线性。与传统的变分原理不同，在这种方法中，在这种方法中提供了上限，而是获得下限。通过处理几维自旋$ 1/2 $ hamiltonians，我们证明了这种方法产生远程相关性的能力，以及一种融合确切结果的基态能量。讨论了可能的扩展，包括到高度激发的状态。
We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large Hilbert space is circumvented by approximating the positivity of the density matrix, order-by-order, in a way that keeps track of a limited set of correlation functions. In particular, the density-matrix description is replaced by a correlation matrix whose dimension is kept linear in system size, to all orders of the approximation. Unlike the conventional variational principle which provides an upper bound on the ground-state energy, in this approach one obtains a lower bound instead. By treating several one-dimensional spin $1/2$ Hamiltonians, we demonstrate the ability of this approach to produce long-range correlations, and a ground-state energy that converges to the exact result. Possible extensions, including to higher-excited states are discussed.
