Approximate diagonalization method for many-fermion Hamiltonians

TL;DR

This paper introduces a new formalism for approximating the diagonalization of many-fermion Hamiltonians, managing errors and divergences by systematically discarding interactions, and enabling hierarchical methods for eigenvalue calculation.

Contribution

A novel formalism that allows controlled approximation of many-fermion Hamiltonians through a hierarchy of diagonalization methods, reducing errors and avoiding divergences.

Findings

Hierarchical diagonalization methods with increasing accuracy

Formalism manages errors and prevents divergences during approximation

Direct calculation of eigenvalues from simplified Hamiltonians

Abstract

The limits of direct unitary transformation of many-fermion Hamiltonians are explored. Practical application of such transformations requires that effective many-body interactions be discarded over the course of a calculation. The truncation of the Hamiltonian leads to finite errors and in some cases divergences. A new formalism is proposed to manage errors and avoid divergences. Removing all interactions from a many-fermion Hamiltonian reduces it to fermion number operators allowing for direct calculation of eigenvalues. If the same transformations are applied to the bare fermions, eigenfermions are produced whose Slater determinants form eigenstates. This enables a hierarchy of diagonalization methods of increasing accuracy as fewer interactions are discarded from the Hamiltonian.