Calculating eigenvalues and eigenvectors of parameter-dependent hamiltonians using an adaptative wave operator method

TL;DR

This paper introduces an adaptive wave operator method for efficiently computing eigenvalues and eigenvectors of large, parameter-dependent Hamiltonians, including non-Hermitian cases, with applications in molecular photodissociation.

Contribution

The paper presents a novel adaptive wave operator algorithm that dynamically follows eigenspaces as parameters change, improving efficiency over fixed active space methods.

Findings

Converges within a few dozen iterations

Handles non-Hermitian Hamiltonians effectively

Successfully applied to molecular photodissociation models

Abstract

We propose a wave operator method to calculate eigenvalues and eigenvectors of large parameter-dependent matrices, using an adaptative active subspace. We consider a hamiltonian which depends on external adjustable or adiabatic parameters, using adaptative projectors which follow the successive eigenspaces when the adjustable parameters are modified. The method can also handle non-hermitian hamiltonians. An iterative algorithm is derived and tested through comparisons with a standard wave operator algorithm using a fixed active space and with a standard block-Davidson method. The proposed approach is competitive, it converges within a few dozen iterations at constant memory cost. We first illustrate the abilities of the method on a 4-D coupled oscillator model hamiltonian. A more realistic application to molecular photodissociation under intense laser fields with varying intensity or frequency is also presented. Maps of photodissociation resonances of H${}_2^+$ in the vicinity of exceptional points are calculated as an illustrative example.