The Spectrum of the two dimensional Hubbard model at low filling

TL;DR

This paper calculates the exact energy spectrum of the 2D Hubbard model at low filling, revealing residual degeneracies and unexpected spectral properties that suggest a hidden symmetry beyond known group theoretical symmetries.

Contribution

It provides the first detailed spectral analysis of the 2D Hubbard model with full symmetry considerations, uncovering evidence for a potential unknown symmetry.

Findings

Residual degeneracies suggest a hidden symmetry.

Spectral statistics are close to random matrix theory but not exact.

Level velocity correlations decay exponentially, differing from RMT predictions.

Abstract

Using group theoretical and numerical methods we have calculated the exact energy spectrum of the two-dimensional Hubbard model on square lattices with four electrons for a wide range of the interaction strength. All known symmetries, i.e.\ the full space group symmetry, the SU(2) spin symmetry, and, in case of a bipartite lattice, the SU(2) pseudospin symmetry, have been taken explicitly into account. But, quite remarkably, a large amount of residual degeneracies remains giving strong evidence for the existence of a yet unknown symmetry. The level spacing distribution and the spectral rigidity are found to be in close to but not exact agreement with random matrix theory. In contrast, the level velocity correlation function presents an unexpected exponential decay qualitatively different from random matrix behavior.