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arXiv:2203.00227 · Physical review. B./Physical review. B

C3 symmetry breaking metal-insulator transitions in a flat band in the half-filled Hubbard model on the decorated honeycomb lattice

H. L. Nourse, Ross H. McKenzie, Benjamin James Powell

Published May 16, 2022• 3 citations
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Abstract

We study the single-orbital Hubbard model on the half-filled decorated honeycomb lattice. In the noninteracting theory at half filling the Fermi energy lies within a flat band where strong correlations are enhanced. The lattice is highly frustrated. We find a correlation driven first-order metal-insulator transition to two different insulating ground states---a dimer valence bond solid Mott insulator when intertriangle correlations dominate, and a broken ${C}_{3}$-symmetry antiferromagnet that arises from frustration when intratriangle correlations dominate. The metal-insulator transitions into these two phases have very different characters. The metal-broken ${C}_{3}$ antiferromagnetic transition is driven by spontaneous ${C}_{3}$ symmetry breaking that lifts the topologically required degeneracy at the Fermi energy and opens an energy gap in the quasiparticle spectrum. The metal-dimer valence bond solid transition breaks no symmetries of the Hamiltonian. It is caused by strong correlations renormalizing the electronic structure into a phase that is adiabatically connected to both the trivial band insulator and the ground state of the spin-1/2 Heisenberg model in the relevant parameter regime. Therefore, neither of these metal-insulator transitions can be understood in either the Brinkmann-Rice or Slater paradigms.

DOI
10.1103/physrevb.105.205119

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We study the single-orbital Hubbard model on the half-filled decorated honeycomb lattice. In the noninteracting theory at half filling the Fermi energy lies within a flat band where strong correlations are enhanced. The lattice is highly frustrated. We find a correlation driven first-order metal-insulator transition to two different insulating ground states---a dimer valence bond solid Mott insulator when intertriangle correlations dominate, and a broken C3{C}_{3}C3​-symmetry antiferromagnet that arises from frustration when intratriangle correlations dominate. The metal-insulator transitions into these two phases have very different characters. The metal-broken C3{C}_{3}C3​ antiferromagnetic transition is driven by spontaneous C3{C}_{3}C3​ symmetry breaking that lifts the topologically required degeneracy at the Fermi energy and opens an energy gap in the quasiparticle spectrum. The metal-dimer valence bond solid transition breaks no symmetries of the Hamiltonian. It is caused by strong correlations renormalizing the electronic structure into a phase that is adiabatically connected to both the trivial band insulator and the ground state of the spin-1/2 Heisenberg model in the relevant parameter regime. Therefore, neither of these metal-insulator transitions can be understood in either the Brinkmann-Rice or Slater paradigms.
We study the interplay of strong electron correlations and intratriangle 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 intratriangle multiorbital 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 UUU 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\'eel ordered.
The single-orbital Hubbard model is often a good description of the low energy dynamics of strongly correlated electron systems. Importantly, the single-orbital Hubbard model at half-filling is able to capture the Mott metal-insulator transition that occurs in many materials. However, there are insulating phases (as well as other exotic phases) that occur due to strong electronic correlations in materials that are away from half-filling. In many cases, these additional phases occur because the constituent electrons of the material come from multi-orbital atomic environments that require more complicated descriptions such as the multi-orbital Hubbard model. In other cases, as we show in this thesis, the rich phase diagram arises from the underlying lattice because of special geometric features.For example, decorated lattices, which often occur in organometallics (e.g., metal-organic frameworks (MOFs)), have geometrical complexity due to the molecular structures that decorate the lattice. We argue that the effective description for many of these materials is the single-orbital Hubbard model. Yet, these materials still have rich phase diagrams because the molecular structures of the material cause effective multi-orbital interactions generated from the local Coulomb interaction.We investigate the single-orbital Hubbard model on the decorated honeycomb lattice at zero temperature using rotationally invariant slave-boson (RISB) theory in the mean-field approximation, at a range of fillings. Numerous metal-insulator transitions occur - the insulating phases include a real-space Mott insulator, a dimer Mott insulator, a trimer Mott insulator, flat-band ferromagnets, and a spin-1 Mott insulator, dominated by spin-triplet fluctuations. This menagerie of phases is caused by effective multi-orbital interactions arising from the interplay of electronic correlations, lattice structure, and band filling effects. For example, with only on-site Coulomb interactions, the spin-1 Mott insulator is driven by an effective Hund's coupling on a three-site ring that favors the formation of triplets when the three-site ring has four electrons. We argue that this exotic phase may be realized in layers of the organometallic molecular crystal Mo3S7(dmit)3.
We report 10 ground states arising from strong correlations in the single-orbital Hubbard model on the decorated honeycomb lattice, including Dirac metals, flat-band ferromagnets, real-space Mott insulators, dimer and trimer Mott insulators, and a spin-1 Mott insulator. The rich phase diagram arises from structures within the unit cell. Hence, such states are absent on simpler lattices. We argue that such insulating phases are prevalent on decorated lattices. These are found in many materials and common in coordination polymers, providing a playground to explore this physics.
We study the metal-insulator transition in the half-filled Hubbard model on a Kagome lattice using the variational cluster approximation. The strong coupling limit of the model corresponds to the S=1/2S=1/2S=1/2 Kagome Heisenberg antiferromagnet, which is known to have a singlet ground state, although its detail is still debated. As the results of the cluster methods generally depend much on the choice of the unit cluster, we have chosen the clusters that are compatible with these singlet ground states in the strong coupling case found so far, which basically consist of even number of sites. It is found that the correlated electrons on the Kagome lattice have a strong tendency to form valence-bond structures, which are the resonation of electrons on a single bond or several bonds forming loops. The zero-temperature metal-insulator transition at some interaction strength is possibly driven by the formation of such short range valence bonds and shows a second order character, which is distinctive from the Brinkman-Rice scenario. The electrons on these valence bonds further localizes onto each site as the interaction increases, and the valence bonds of electrons finally turn into magnetic singlet bonds between localized S=1/2S=1/2S=1/2 spins, which are consistent with the ground states of the Kagome antiferromagnet.
Employing extensive cellular dynamical mean-field theory calculations with an exact diagonalization impurity solver, we investigate the ground-state phase diagrams and nonmagnetic metal-insulator transitions of the half-filled Hubbard model on two plaquette (the 1/5 depleted and checkerboard) square lattices. We identify three different insulators in the phase diagrams: dimer insulator, antiferromagnetic insulator, and plaquette insulator. We also demonstrate that the plaquette insulator is a novel fragile Mott insulator (FMI) which features a nontrivial one-dimensional irreducible representation of the C4v{C}_{4v}C4v​ crystalline point group and cannot be adiabatically connected to any band insulator with time-reversal symmetry. Furthermore, we study the nonmagnetic quantum phase transitions from the metal to the FMI and find that this Mott metal-insulator transition is characterized by the splitting of the noninteracting bands due to interaction effects.
We present a comprehensive computational study of the phase diagram of the frustrated S=1/2S=1/2S=1/2 Heisenberg antiferromagnet on the honeycomb lattice, with second-nearest (J2)({J}_{2})(J2​) and third-neighbor (J3)({J}_{3})(J3​) couplings. Using a combination of exact diagonalizations (EDs) of the original spin model, of the Hamiltonian projected into the nearest-neighbor short-range valence-bond basis, and of an effective quantum dimer model, as well as a self-consistent cluster mean-field theory, we determine the boundaries of several magnetically ordered phases in the region ${J}_{2},{J}_{3}\ensuremath{\in}[0,1]$, and find a sizable magnetically disordered region in between. We characterize part of this magnetically disordered phase as a plaquette valence-bond crystal phase. At larger J2{J}_{2}J2​, we locate a sizable region in which staggered valence-bond crystal correlations are found to be important, either due to genuine valence-bond crystal (VBC) ordering or as a consequence of magnetically ordered phases, which break lattice rotational symmetry. Furthermore, we find that a particular parameter-free Gutzwiller projected tight-binding wave function has remarkably accurate energies compared to finite-size extrapolated ED energies along the transition line from conventional N\'eel to plaquette VBC phases, a fact that points to possibly interesting critical behavior---such as a deconfined critical point---across this transition. We also comment on the relevance of this spin model to model the spin liquid region found in the half filled Hubbard model on the honeycomb lattice.