A Perturbative Density Matrix Renormalization Group Algorithm for Large Active Spaces.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Many-Body Theory

Background:

• Variational density matrix renormalization group (DMRG) is a standard algorithm for quantum systems.
• Standard DMRG becomes computationally expensive for systems with very large active spaces.

Purpose of the Study:

• Introduce a low-cost computational method, p-DMRG (perturbative DMRG), as an alternative to variational DMRG.
• Develop an efficient tool for benchmark studies of quantum systems with large active spaces.

Main Methods:

• p-DMRG combines a low-bond-dimension DMRG calculation for a zeroth-order wave function with second-order perturbation theory.
• The first-order wave function is represented as a sum of matrix product states to save computational cost and memory.
• Extrapolation schemes are proposed to minimize errors in wave function calculations.

Main Results:

• p-DMRG achieves ground state energies comparable to variational DMRG with large bond dimensions.
• The method demonstrates significant savings in computational cost and memory requirements.
• Numerical results for Cr2 and 1,3-butadiene validate the efficiency and accuracy of p-DMRG.

Conclusions:

• p-DMRG offers a computationally efficient and accurate approach for studying quantum systems, particularly those with large active spaces.
• The method is a promising tool for future benchmark studies in quantum chemistry and physics.