Interaction-driven phases in the half-filled spinless honeycomb lattice from exact diagonalization

Abstract

We investigate the fate of interaction-driven phases in the half-filled honeycomb lattice for finite systems via exact diagonalization with nearest-and next-nearest-neighbor interactions. We find evidence for a charge density wave phase, a Kekulé bond order, and a sublattice charge-modulated phase in agreement with previously reported mean-field phase diagrams. No clear sign of an interaction-driven Chern insulator phase (Haldane phase) is found despite being predicted by the same mean-field analysis. We characterize these phases by their ground-state degeneracy and by calculating charge-order and bond-order correlation functions.

Fate of interaction-driven topological insulators under disorder

“…These states of matter possess both conventional order, characterized by an order parameter and a broken symmetry, and protected edge states associated with a topological quantum number. Interactiondriven QAH and QSH phases were first conceived in the context of 2D honeycomb lattice Dirac fermions [10] assuming sufficiently strong electronic repulsions although more recent analytical and numerical works question the proposal for this particular model [11][12][13][14].On the contrary, it has been proposed that 2D systems with a quadratic band crossing point (QBCP) are unstable to electronic correlation because of the finite density of states at the Fermi level leading to the possibility of The relationship between fixed points QAH and QAH-II is provided in the inset figure of Fig. 2(a).…”

Exotic magnetic orderings in the kagome Kondo-lattice model

“…However, relatively large electron-electron Coulomb interactions are required to induce chiral states due to the vanishing density of electron states. [14,15].…”

Interaction-Driven Spontaneous Quantum Hall Effect on a Kagome Lattice

“…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.…”

“…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.…”