Liao Ke, Zhai Huanchen, Christlmaier Evelin Martine Corvid, Schraivogel Thomas, Ríos Pablo López, Kats Daniel, Alavi Ali
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, United States.
Max Planck Institute for Solid State Research, Heisenbergstrasse 1, 70569 Stuttgart, Germany.
J Chem Theory Comput. 2023 Mar 28;19(6):1734-1743. doi: 10.1021/acs.jctc.2c01207. Epub 2023 Mar 13.
We present the theory of a density matrix renormalization group (DMRG) algorithm which can solve for both the ground and excited states of non-Hermitian transcorrelated Hamiltonians and show applications in molecular systems. Transcorrelation (TC) accelerates the basis set convergence rate by including known physics (such as, but not limited to, the electron-electron cusp) in the Jastrow factor used for the similarity transformation. It also improves the accuracy of approximate methods such as coupled cluster singles and doubles (CCSD) as shown by recent studies. However, the non-Hermiticity of the TC Hamiltonians poses challenges for variational methods like DMRG. Imaginary-time evolution on the matrix product state (MPS) in the DMRG framework has been proposed to circumvent this problem, but this is currently limited to treating the ground state and has lower efficiency than the time-independent DMRG (TI-DMRG) due to the need to eliminate Trotter errors. In this work, we show that with minimal changes to the existing TI-DMRG algorithm, namely, replacing the original Davidson solver with the general Davidson solver to solve the non-Hermitian effective Hamiltonians at each site for a few low-lying right eigenstates, and following the rest of the original DMRG recipe, one can find the ground and excited states with improved efficiency compared to the original DMRG when extrapolating to the infinite bond dimension limit in the same basis set. An accelerated basis set convergence rate is also observed, as expected, within the TC framework.
我们提出了一种密度矩阵重整化群（DMRG）算法理论，该算法可求解非厄米转相关哈密顿量的基态和激发态，并展示其在分子系统中的应用。转相关（TC）通过在用于相似变换的约斯屈罗因子中纳入已知物理（如但不限于电子 - 电子尖点）来加速基组收敛速度。最近的研究表明，它还提高了诸如耦合簇单双激发（CCSD）等近似方法的精度。然而，TC哈密顿量的非厄米性给像DMRG这样的变分方法带来了挑战。有人提出在DMRG框架下对矩阵乘积态（MPS）进行虚时演化来规避这个问题，但目前这仅限于处理基态，并且由于需要消除 Trotter 误差，其效率低于与时间无关的DMRG（TI - DMRG）。在这项工作中，我们表明，对现有的TI - DMRG算法进行最小的改动，即使用通用戴维森求解器代替原来的戴维森求解器，以求解每个位点上的非厄米有效哈密顿量的几个低阶右本征态，并遵循原始DMRG算法的其余部分，在相同基组下外推到无限键维度极限时，与原始DMRG相比，可以以更高的效率找到基态和激发态。正如预期的那样，在TC框架内也观察到了加速的基组收敛速度。
