Stochastic determination of effective Hamiltonian for the full configuration interaction solution of quasi-degenerate electronic states

TL;DR

This paper introduces a quantum Monte Carlo method that efficiently and accurately computes effective Hamiltonians for quasi-degenerate electronic states, addressing challenges like the sign problem in complex quantum systems.

Contribution

A novel stochastic quantum Monte Carlo approach for effective Hamiltonian calculation that handles quasi-degenerate states with reduced sign problem.

Findings

Successfully applied to H4 and N2 models with quasi-degeneracy

Accurately captures electronic states near dissociation limits

Demonstrates improved efficiency over traditional methods

Abstract

We propose a novel quantum Monte Carlo method in configuration space, which stochastically samples the contribution from a large secondary space to the effective Hamiltonian in the energy dependent partitioning of L\"owdin. The method treats quasi-degenerate electronic states on a target energy with bond dissociations and electronic excitations avoiding significant amount of the negative sign problem. The performance is tested with small model systems of H$_4$ and N$_2$ at various configurations with quasi-degeneracy.