Characterizing Mott Insulators in the Interacting One-Body Picture

TL;DR

This paper develops a framework combining symmetry analysis, reduced density matrices, and tensor network methods to characterize Mott insulators in the interacting one-body picture, applied to the Hubbard diamond chain.

Contribution

It introduces a novel approach integrating symmetry classification, reduced density matrices, and tensor network techniques to analyze Mott insulating phases.

Findings

Identification of three distinct phases and their transitions.

Symmetry-labelled spectral functions effectively characterize insulating phases.

The combined approach offers accessible tools for studying correlation-driven insulators.

Abstract

We present a framework to characterize Mott insulating phases within the interacting one-body picture, focusing on the Hubbard diamond chain featuring both Hubbard interactions and spin-orbit coupling simulated within cellular dynamical mean field theory. Using symmetry analysis of the single-particle Green's function, we classify spectral functions by irreducible representations at high-symmetry points of the Brillouin zone. Complementarily, we calculate the one-body reduced density matrix which allows us to reach both a qualitative description of charge distribution and an analysis of the state purity. Moreover, within the Tensor Network framework, we employ a Density Matrix Renormalization Group approach to confirm the presence of three distinct phases and their corresponding phase transitions. Our results highlight how symmetry-labelled spectral functions and effective orbital analysis provide accessible single-particle tools for probing correlation-driven insulating phases.