Spin-$0$ Mott insulator to metal to spin-$1$ Mott insulator transition in the single-orbital Hubbard model on the decorated honeycomb lattice

TL;DR

This paper investigates how strong electron correlations and intra-triangle spin exchange influence phase transitions in a single-orbital Hubbard model on a decorated honeycomb lattice, revealing a transition from spin-0 to spin-1 Mott insulators mediated by antiferromagnetic exchange.

Contribution

It introduces a detailed analysis of the phase diagram showing spin-0 and spin-1 Mott insulators and their connection to intra-triangle interactions and magnetic order in the Hubbard model.

Findings

Identification of a transition from spin-0 to spin-1 Mott insulators driven by spin exchange.

Characterization of magnetic order in the spin-1 Mott insulator as Ne9el order.

Demonstration of a spin-1 Slater insulator with antiferromagnetic order at small U.

Abstract

We study the interplay of strong electron correlations and intra-triangle spin exchange at two-thirds filling of the single-orbital Hubbard model on the decorated honeycomb lattice using rotationally invariant slave bosons. We find that the spin exchange tunes between a spin-$1$ Mott insulator, a metal, and a spin-$0$ Mott insulator when the exchange is antiferromagnetic. The Mott insulators occur from effective intra-triangle multi-orbital interactions and are adiabatically connected to the ground state of an isolated triangle. An antiferromagnetic spin exchange, as determined by the Goodenough-Kanamori rules, may occur in coordination polymers from kinetic exchange via the ligands. We characterize the magnetism in the regime where spin-triplets dominate. For small $U$ a spin-$1$ Slater insulator occurs with antiferromagnetic order between triangles. Magnetism in the spin-$1$ Mott insulator is described by a spin-$1$ Heisenberg model on a honeycomb lattice, whose ground state is N\'{e}el ordered.