Metal-Insulator Transition of Fermions on a Kagome Lattice at 1/3 Filling

Abstract

We discuss the metal-insulator transition of the spinless fermion model on a kagome lattice at 1/3 filling. The system is analyzed by using exact diagonalization, density-matrix renormalization group methods, and random-phase approximation. In the strong-coupling region, the charge-ordered ground state is consistent with the predictions of an effective model, i.e., plaquette order. We find that the qualitative properties of the metal-insulator transition are totally different depending on the sign of the hopping matrix elements, reflecting the difference in the band structure near the Fermi level.

Phase diagram of the13-filled extended Hubbard model on the kagome lattice

“…Four phases have been obtained in the (V, U ) plane, the semi-metal (SM), a charge density wave (CDW), a spin charge density wave (SCDW), and a pinned metal droplet phase (PMD). As already mentioned, the first two phases have already been reported elsewhere 37,44,45 . For the CDW, a perturbative effective model of order t 3 /V 2 maps the present model onto a quantum dimer model on the hexagonal lattice 11,37,44,45 .…”

“…Indeed, in the classical limit t = 0 and V = 0, the ground state is macroscopically degenerate, and the configurations that minimize the energy obey a rule of two electrons per triangle with one doubly occupied site. A finite t lifts this degeneracy and in the limit t ≪ V the system is effectively described by a hardcore quantum dimer model (QDM) on the honeycomb lattice 11,37,44 whose ground state consists of resonating plaquettes. The mean-field treatment cannot capture the resonating plaquettes of the QDM, but its solution can be thought of as its electrostatic counterpart 10 .…”

“…In particular, the 1/3-filled system takes a special role since, in the non-interacting limit, the Fermi sea is at the Dirac cones at the corner of the Brillouin zone (the K point) and the ground state (GS) is a semi-metal (SM). With interactions, let us cite studies on topological phases 10 , Mottinsulator transitions for spinless fermions 37 or fractionalization of defects with an extra bow-tie term 7 . Under the presence of the Hubbard interaction, spin charge density waves with antiferromagnetic spin stripes are stabilized 10 , but this phase was enforced to preserve the translations.…”

Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice

“…This subject has attracted vigorous research due to support from mean-field studies, followed by low-energy renormalization-group analysis [13,16], and the existence of such topological phases has been suggested for the extended Hubbard model on various lattice models [17][18][19][20][21][22][23][24][25][26][27][28][29][30]. However, unbiased numerical simulations, such as exact diagonalization (ED) and density-matrix renormalization-group (DMRG) studies, found competing states other than topological phases as the true ground states in all previously proposed systems with Dirac points [31][32][33][34] or quadratic band touching points [35,36]. A major obstacle is that, instead of triggering the desired spontaneous TRS breaking, strong interactions tend to stabilize competing solid orders by breaking the translational or rotational lattice symmetry.…”

“…A major obstacle is that, instead of triggering the desired spontaneous TRS breaking, strong interactions tend to stabilize competing solid orders by breaking the translational or rotational lattice symmetry. Thus, the putative topological phase is usually preempted by various competing states [31][32][33][34][35][36]. Moreover, it is also technically challenging to detect such exotic phases with spontaneous TRS breaking, as the TRS partners usually tend to couple on finite-size systems.…”