Characterizing Mott Insulators in the Interacting One-Body Picture

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.

💡 Research Summary

In this work the authors develop a unified single‑particle framework for identifying and characterizing Mott insulating phases in a one‑dimensional Hubbard diamond chain that also hosts a symmetry‑allowed spin‑orbit coupling (SOC). The study combines analytical group‑theoretical analysis of the complex‑frequency single‑particle Green’s function (SPGF) with numerical many‑body techniques—tensor‑network density‑matrix renormalization group (DMRG) and cellular dynamical mean‑field theory (CDMFT) solved by exact diagonalization.

The theoretical part begins by invoking Wigner’s theorem and Schur’s lemma to show that any unitary symmetry of the many‑body Hamiltonian induces a unitary representation on the fermionic operators, which in turn forces the SPGF to satisfy G(z)=U G(z) U†. By block‑diagonalising G(k,z) according to the irreducible representations (irreps) of the little group Gk at each crystal momentum, the authors prove that the spectral function A(k,ω)=−Im G(k,ω)/π can be decomposed into symmetry‑labelled sectors. This decomposition is exact for any complex frequency and provides a powerful diagnostic: different interacting phases manifest distinct patterns of weight among the irreps at high‑symmetry points (Γ, X, …).

Next, the one‑body reduced density matrix (1RDM) γ is introduced. At zero temperature γ can be obtained directly from the SPGF via a contour integral γμν=∮dz/(2πi) Gμν(z). Diagonalising γ yields eigenvalues pj∈