含时密度矩阵重正化群的理论与应用

Theory and Applications of Time Dependent Density Matrix Renormalization Group

密度矩阵重正化群(DMRG)作为计算低维强关联体系强有力的方法为人熟知,在量子化学电子结构计算中得到广泛应用.最近几年,含时密度矩阵重正化群(TD-DMRG)的理论取得较快发展,TD-DMRG逐渐成为复杂体系量子动力学理论模拟的重要新兴方法之一.本文综述了基于矩阵乘积态(MPS)和矩阵乘积算符(MPO)的DMRG基本理论,并重点介绍了若干最常见的TD-DMRG时间演化算法,包括基于演化再压缩(P&C)的算法、基于含时变分原理(TDVP)的算法和时间步瞄准(TST)算法;还对利用TD-DMRG模拟有限温体系的纯化(Purification)算法和最小纠缠典型量子热态(METTS)算法进行了介绍.最后,对近年TD-DMRG在复杂体系量子动力学中的应用进行了总结.

Density matrix renormalization group(DMRG)is well known as a powerful method to study low-dimensional highly-correlated systems and has been widely used for electronic structure calculation in quan⁃tum chemistry.In recent years,the theory of time dependent DMRG(TD-DMRG)has developed rapidly and TD-DMRG has gradually emerged as one of the most important methods of quantum dynamics simulation for complex systems.This review briefly sketches the basic theory of DMRG in the language of matrix product states(MPS)and matrix product operators(MPO),and discusses several most common TD-DMRG time evolu⁃tion algorithms at length,including the propagation and compression(P&C)algorithm,algorithms based on time dependent variational principle(TDVP),and the time step targeting(TST)algorithm.This review also introduces the purification algorithm and minimally entangled typical thermal states(METTS)algorithm that enable TD-DMRG to study the finite temperature effect and summarizes the recent applications of TD-DMRG in quantum dynamics of complex systems.