An important scientific idea is that simple rules can produce complex behaviour. In condensed matter theory, model Hamiltonians with just a few parameters can have rich phase diagrams with many competing ground states. My colleagues and I just completed a paper that is one more example of this.
Spin-0 Mott insulator to metal to spin-1 Mott insulator transition in the single-orbital Hubbard model on the decorated honeycomb lattice H. L. Nourse, Ross H. McKenzie, B. J. Powell
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 (RISB). 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 Néel ordered.
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