Excited-state DMRG made simple with FEAST

TL;DR

This paper presents DMRG[FEAST], a novel method combining FEAST and DMRG to efficiently and reliably compute excited states in many-body quantum systems, overcoming previous limitations.

Contribution

The paper introduces DMRG[FEAST], a new algorithm that stabilizes and improves excited-state calculations within the DMRG framework using the FEAST approach.

Findings

Successfully computed vibrational excitation energies for molecules with 30 degrees of freedom.

Demonstrated stability and reliability in optimizing both low- and high-energy eigenstates.

Outperformed existing excited-state DMRG algorithms in accuracy and stability.

Abstract

We introduce DMRG[FEAST], a new method for optimizing excited-state many-body wave functions with the density matrix renormalization group (DMRG) algorithm. Our approach applies the FEAST algorithm, originally designed for large-scale diagonalization problems, to matrix product state wave functions. We show that DMRG[FEAST] enables the stable optimization of both low- and high-energy eigenstates, therefore overcoming the limitations of state-of-the-art excited-state DMRG algorithms. We demonstrate the reliability of DMRG[FEAST] by calculating anharmonic vibrational excitation energies of molecules with up to 30 fully coupled degrees of freedom.