Suppression of topological Mott-Hubbard phases by multiple charge orders in the honeycomb extended Hubbard model

Abstract

We investigate the competition between charge-density-wave (CDW) states and a Coulomb interaction-driven topological Mott insulator (TMI) in the honeycomb extended Hubbard model. For the spinful model with on-site (U ) and next-nearest-neighbor (V2) Coulomb interactions at half filling, we find two peculiar six-sublattice charge-density-wave insulating states by using variational Monte Carlo simulations as well as the Hartree-Fock approximation. We observe that conventional ordered states always win with respect to the TMI. The ground state is given in the large-V2 region by a CDW characterized by a 220200 (001122) charge configuration for smaller (larger) U , where 0, 1, and 2 denote essentially empty, singly occupied, and doubly occupied sites. Within the 001122-type CDW phase, we find a magnetic transition driven by an emergent coupled-dimer antiferromagnet on an effective square lattice of singly occupied sites. Possible realizations of the found states are discussed.

Two‐Particle Self‐Consistent Method for the Multi‐Orbital Hubbard Model

“…In strongly correlated electronic systems the development of many‐body techniques is driven by the fact that a description of electronic properties in terms of an independent electron picture fails. Correlation effects result in a plethora of fascinating phenomena such as unconventional superconductivity, [ 1–11 ] Mott metal‐to‐insulator transition, [ 12–19 ] non‐Fermi liquid behavior, [ 20–22 ] or spin liquid phases [ 23–29 ] to mention a few. In many materials, correlations originate from a few partially filled orbitals around the Fermi level and, early on, a simplified low‐energy description of those orbitals was proposed in terms of the Hubbard model, [ 13,30–32 ] which maps the electronic part of the full Hamiltonian of the interacting system onto an effective lattice model.…”

Hidden charge order of interacting Dirac fermions on the honeycomb lattice

“…Instead, the fermion residue remains finite across the transition. This hidden charge order eluded previous numerical studies [13][14][15][16][17][18][19][20][21][22] that identified phase transitions through the opening of a Mott gap. The onset of semi-Dirac behaviour may be resolved in large-scale DMRG simulations on infinite cylinders, which are now capable of extracting the momentumdependent excitation spectra of Dirac materials [37].…”

“…While in this case the transition is likely to belong to the chiral Ising GNY universality class, we expect to see a characteristic crossover in the critical fluctuations due the proximity to the unusual critical point at V 1 = 0. It has been suggested [22] that the regime of dominant V 2 could become experimentally accessible by using silicon adatoms or cold atoms in doublelayers of triangular optical lattices.…”

Criticality of Dirac fermions in the presence of emergent gauge fields

“…This model has attracted a lot of attention because of the suggestion [32] that second-neighbor interactions V 2 could stabilize topological Mott phases, as described by the Haldane model [33]. Extensive numerical [34][35][36][37][38][39][40][41][42][43][44] and analytical [45] efforts have concluded, however, that fluctuations beyond mean-field theory lead to a direct transition from the Dirac semimetal to charge-density wave order (CDW 3 ) with a threefold increased unit cell (see Fig. 1).…”

“…It has been suggested [44] that the regime of dominant V 2 could become accessible in cold-atom experiments [46] by engineering optical lattices in which the triangular sublattices of the honeycomb lattice are spatially separated into a bilayer structure. This is also what happens naturally in two-dimensional (2D) materials like silicene and germanene, which are chemically similar to graphene but are realized in a buckled lattice with triangular sublattices at different heights [47].…”