Full Spin and Spatial Symmetry Adapted Technique for Correlated Electronic Hamiltonians: Application to an Icosahedral Cluster

TL;DR

This paper introduces a novel hybrid computational technique that fully exploits spin and spatial symmetries of electronic Hamiltonians with non-Abelian point groups, enabling exact solutions for large, complex systems like an icosahedral cluster.

Contribution

The authors develop a general, symmetry-adapted method combining Valence Bond and spin basis techniques applicable to any point group, demonstrated on a large icosahedral system.

Findings

Successfully applied to a 1.78 million dimensional Hilbert space

Revealed excited states of an icosahedral cluster

Method applicable to finite temperature properties of correlated systems

Abstract

One of the long standing problems in quantum chemistry had been the inability to exploit full spatial and spin symmetry of an electronic Hamiltonian belonging to a non-Abelian point group. Here we present a general technique which can utilize all the symmetries of an electronic (magnetic) Hamiltonian to obtain its full eigenvalue spectrum. This is a hybrid method based on Valence Bond basis and the basis of constant z-component of the total spin. This technique is applicable to systems with any point group symmetry and is easy to implement on a computer. We illustrate the power of the method by applying it to a model icosahedral half-filled electronic system. This model spans a huge Hilbert space (dimension 1,778,966) and in the largest non-Abelian point group. The $C_{60}$ molecule has this symmetry and hence our calculation throw light on the higher energy excited states of the bucky ball. This method can also be utilized to study finite temperature properties of strongly correlated systems within an exact diagonalization approach.