Characterizing Mott Insulators in the Interacting One-Body Picture

TL;DR

The paper develops a framework to characterize correlation-driven Mott insulating phases through symmetry-labelled single-particle Green's functions and 1RDM analysis, applied to the interacting Hubbard Diamond Chain with SOC. It combines tensor-network (DMRG) methods and cellular dynamical mean-field theory to identify three distinct phases and their transitions, and shows how irrep decomposition of spectral functions and effective one-body orbitals illuminate the microscopic content of each phase. Key findings include phase-dependent changes in spectral weight distribution at high-symmetry points, evolution of effective orbitals across phases, and a discontinuous 1RDM purity signaling transitions between Mott and SOC-induced insulating regimes. The approach provides a practical, experimentally accessible route to probe correlation-driven insulating behavior and establishes a link between symmetry, Green’s functions, and emergent orbital degrees of freedom with potential relevance to real materials and ARPES data.

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.

Figures (10)

• Figure 1: The Hubbard diamond chain (space group 47). Each site contains one spinful s-like orbital.
• Figure 2: The cluster and bath configuration of the effective AIM solved via ED. 4 sites are used per irrep($A/B$) of C$_2$. The relative signs of the hybridizations are indicated in red adjacent to the respective lines.
• Figure 3: Energy gap between the four-particle ground state and the first excited state, and expectation value of the mirror operator, as functions of $U$ and $\phi$. (a) – (b) Energy gap for $t_2/|t_1| = 0.5$ and $t_2/|t_1| = 0.8$, respectively. The dotted lines indicate the regions where the gap closes. (c) – (d) Expectation value of the mirror operator for $t_2/|t_1| = 0.5$ and $t_2/|t_1| = 0.8$ respectively.
• Figure 4: Representative spectral functions for each phase at $U=4$. The side-panels represent the spectral weight at the high symmetry points separated by irrep of the little group.
• Figure 5: Effective one-body orbitals of the occupied states for all phases at $U=4$. Classical probability is indicated in the center of each orbital. Amplitude and phase of the orbital components associated with each site are represented by the radius and the colour of the circle at each orbital site.