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Summary

We developed improved dynamical density matrix renormalization group (DDMRG) algorithms for accurate calculations of correlated systems. These enhanced methods, DDMRG++ and td-DMRG++, improve precision for molecular and material properties.

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Area of Science:

Quantum chemistry
Computational physics
Materials science

Background:

Accurate computation of dynamical correlation functions is crucial for understanding correlated quantum systems.
Existing methods like DDMRG and td-DMRG have limitations in accuracy and efficiency.
Ab initio calculations require robust algorithms to capture electron correlation effects.

Purpose of the Study:

To improve the accuracy and efficiency of ab initio dynamical correlation function calculations.
To develop enhanced formulations of DDMRG and td-DMRG algorithms.
To apply these improved methods to challenging problems in molecular and materials science.

Main Methods:

Development and application of DDMRG++ and td-DMRG++ algorithms.
Analysis of algorithm performance on small model problems.
Ab initio calculations for molecular systems (water) and extended systems (hydrogen chains).

Main Results:

DDMRG++ and td-DMRG++ provide increased accuracy at the same bond dimension compared to standard methods.
Accurate oxygen core-excitation energy in water was computed, refining coupled cluster results.
Local density of states, gaps, and polarization functions in hydrogen chains were calculated, revealing metallicity and delocalization trends.

Conclusions:

The developed DDMRG++ and td-DMRG++ algorithms offer significant improvements for ab initio dynamical correlation function calculations.
These enhanced methods provide valuable insights into electronic properties of molecules and materials.
The study demonstrates the potential of these advanced DMRG techniques for future research in quantum many-body systems.