论文标题
混合量子状态的密度基质重归其化算法
Density Matrix Renormalization Group Algorithm For Mixed Quantum States
论文作者
论文摘要
密度矩阵重新归一化组（DMRG）算法在计算一维量子多体系统的基础状态方面非常成功。但是，对于与混合量子状态有关的问题，它不太成功，因为这种算法尚不存在，或者它可能返回非物理解决方案。在这里，我们为混合量子状态提出了一个阳性基质产品ANSATZ，该量子均通过构造保留阳性。更重要的是，它允许构建与基础状态的标准DMRG相同的DMRG算法，迭代地将全局优化问题降低到同一类型的本地局部优化问题，其能量在原则上单调地融合。该算法用于计算平衡状态和非平衡稳态，并在数值上证明其优点。
Density Matrix Renormalization Group (DMRG) algorithm has been extremely successful for computing the ground states of one-dimensional quantum many-body systems. For problems concerned with mixed quantum states, however, it is less successful in that either such an algorithm does not exist yet or that it may return unphysical solutions. Here we propose a positive matrix product ansatz for mixed quantum states which preserves positivity by construction. More importantly, it allows to build a DMRG algorithm which, the same as the standard DMRG for ground states, iteratively reduces the global optimization problem to local ones of the same type, with the energy converging monotonically in principle. This algorithm is applied for computing both the equilibrium states and the non-equilibrium steady states, and its advantages are numerically demonstrated.
