The diagonalization of quantum field Hamiltonians

TL;DR

The paper presents a novel diagonalization method called quasi-sparse eigenvector diagonalization that efficiently finds low-energy eigenstates of quantum Hamiltonians using various bases and Hamiltonian types, integrating diagonalization with Monte Carlo techniques.

Contribution

It introduces a new general diagonalization approach applicable to diverse quantum Hamiltonians, combining diagonalization and Monte Carlo methods for improved efficiency.

Findings

Effective in identifying important basis vectors for low-energy states

Applicable to both Hermitian and non-Hermitian Hamiltonians

Works with finite and infinite-dimensional systems

Abstract

We introduce a new diagonalization method called quasi-sparse eigenvector diagonalization which finds the most important basis vectors of the low energy eigenstates of a quantum Hamiltonian. It can operate using any basis, either orthogonal or non-orthogonal, and any sparse Hamiltonian, either Hermitian, non-Hermitian, finite-dimensional, or infinite-dimensional. The method is part of a new computational approach which combines both diagonalization and Monte Carlo techniques.