Excited-State DMRG Made Simple with FEAST.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Many-Body Physics

Background:

• The Density Matrix Renormalization Group (DMRG) is a powerful algorithm for studying quantum many-body systems.
• Optimizing excited-state wave functions presents significant computational challenges, limiting the scope of current DMRG methods.
• Accurate calculation of molecular vibrational energies is crucial for understanding chemical reactions and material properties.

Purpose of the Study:

• To introduce DMRG[FEAST], a new method combining DMRG with the FEAST algorithm for improved excited-state wave function optimization.
• To overcome the limitations of existing excited-state DMRG algorithms in stably optimizing both low- and high-energy eigenstates.
• To demonstrate the reliability of DMRG[FEAST] for calculating anharmonic vibrational excitation energies in complex molecular systems.

Main Methods:

• Integration of the FEAST eigenvalue solver with the DMRG algorithm for matrix product state wave functions.
• Application of the novel DMRG[FEAST] method to optimize excited-state many-body wave functions.
• Calculation of anharmonic vibrational excitation energies for molecules with up to 30 coupled degrees of freedom.

Main Results:

• DMRG[FEAST] enables stable optimization of both low- and high-energy eigenstates.
• The method overcomes limitations of current state-of-the-art excited-state DMRG algorithms.
• Reliable calculation of anharmonic vibrational excitation energies was achieved for complex molecular systems.

Conclusions:

• DMRG[FEAST] represents a significant advancement in computational quantum chemistry and physics.
• The method provides a robust and stable approach for excited-state calculations.
• This technique opens new possibilities for studying complex molecular vibrations and other quantum phenomena.