Abstract Interaction-driven topological phases significantly enrich the class of topological materials and thus are of great importance. Here, we study the phase diagram of interacting spinless fermions filling the two-dimensional checkerboard lattice with a quadratic band touching (QBT) point. By developing new diagnosis based on the state-of-the-art density-matrix renormalization group and exact diagonalization, we determine accurate quantum phase diagram for such a system at half-filling with three distinct phases. For weak nearest-neighboring interactions, we demonstrate the instability of the QBT towards an interaction-driven spontaneous quantum anomalous Hall (QAH) effect. For strong interactions, the system breaks the rotational symmetry realizing a nematic charge-density-wave (CDW) phase. Interestingly, for intermediate interactions we discover a symmetry-broken bond-ordered critical phase sandwiched in between the QAH and CDW phases, which splits the QBT into two Dirac points driven by interaction. Instead of the direct transition between QAH and CDW phases, our identification of an intermediate phase sheds new light on the theoretical understanding of the interaction-driven phases in QBT systems.
We study the quantum phases of spinless fermions at one-third filling on a kagome lattice featuring a quadratic band touching Fermi point. In the presence of weak first and second nearest-neighbor repulsive interactions (
V1 and
V2), we demonstrate an interaction driven quantum anomalous Hall effect by employing exact diagonalization and density-matrix renormalization group methods. The time-reversal symmetry is broken spontaneously by forming loop currents that exhibit long-range correlation. Quantized Hall conductance corresponding to a Chern number of $\ifmmode\pm\else\textpm\fi{}1$ is obtained by measuring the pumped charge through inserting flux in a cylinder geometry. We find that the energy gap, which topologically protects the emerging ground states, can be enhanced remarkably by a moderate
V2<V1 via calculating the spectrum and charge excitation gaps, which highlights the experimentally feasible scheme of realizing the interaction driven topological phase by spatially decaying interactions on topologically trivial lattice models.
We examine the existence of the interaction-generated quantum anomalous Hall phase on the honeycomb lattice. For the spinless model at half-filling, the existence of a quantum anomalous Hall phase (Chern insulator phase) has been predicted using mean-field methods. However, recent exact diagonalization studies for small clusters with periodic boundary conditions have not found a clear sign of an interaction-driven Chern insulator phase. We use the exact diagonalization method to study properties of small clusters with open boundary conditions, and contrary to previous studies, we find clear signatures of the topological phase transition for finite-size clusters. We also examine the applicability of the entangled-plaquette-state (correlator-product-state) ansatz to describe the ground states of the system. Within this approach the lattice is covered with plaquettes and the ground-state wave function is written in terms of the plaquette coefficients. Configurational weights can then be optimized using a variational Monte Carlo algorithm. Using the entangled-plaquette-state ansatz we study the ground-state properties of the system for larger system sizes and show that the results agree with the exact diagonalization results for small clusters. This confirms the validity of the entangled-plaquette-state ansatz to describe the ground states of the system and provides further confirmation of the existence of the quantum anomalous Hall phase in the thermodynamic limit, as predicted by mean-field theory calculations.
We investigate the phase diagram of spinless fermions with nearest- and next-nearest-neighbor density-density interactions on the honeycomb lattice at half-filling. Using exact diagonalization techniques of the full Hamiltonian and constrained subspaces, combined with a careful choice of finite-size clusters, we determine the different charge orderings that occur for large interactions. In this regime, we find a two-sublattice N\'eel-like state, a charge modulated state with a tripling of the unit cell, a zigzag phase, and a charge ordered state with a 12-site unit cell we call N\'eel domain wall crystal, as well as a region of phase separation for attractive interactions. A sizable region of the phase diagram is classically degenerate, but it remains unclear whether an order-by-disorder mechanism will lift the degeneracy. For intermediate repulsion, we find evidence for a Kekul\'e or plaquette bond-order wave phase. We also investigate the possibility of a spontaneous Chern insulator phase (dubbed topological Mott insulator), as previously put forward by several mean-field studies. Although we are unable to detect convincing evidence for this phase based on energy spectra and order parameters, we find an enhancement of current-current correlations with the expected spatial structure compared to the noninteracting situation. While for the studied $t\ensuremath{-}{V}_{1}\ensuremath{-}{V}_{2}$ model, the phase transition to the putative topological Mott insulator is preempted by the phase transitions to the various ordered states, our findings might hint at the possibility for a topological Mott insulator in an enlarged Hamiltonian parameter space, where the competing phases are suppressed.
The interaction-driven quantum anomalous Hall (QAH) insulator has been sought for a long time in a Dirac semimetal with linear band touching points at the Fermi level. By combining exact diagonalization, density matrix renormalization group, and analytical methods, we study a spinless fermion system on the checkerboard lattice with twofold rotational symmetry, which realizes two Dirac band touching points in the absence of interaction. At weak coupling, the Dirac semimetal is stable. At a finite density-density repulsive interaction, we analyze possible symmetry broken states, and find that an QAH state is stabilized when the interaction strength exceeds the energy scale controlling the separation between the Dirac points. Through numerical simulations, we verify the existence of the QAH phase with spontaneous time-reversal symmetry breaking and quantized Chern number
C=1.
We study the quantum phases driven by interaction in a semimetal with a quadratic band touching at the Fermi level. By combining the density matrix renormalization group (DMRG), analytical power expanded Gibbs potential method, and the weak coupling renormalization group, we study a spinless fermion system on a checkerboard lattice at half-filling, which has a quadratic band touching in the absence of interaction. In the presence of strong nearest-neighbor (
V1) and next-nearest-neighbor (
V2) interactions, we identify a site nematic insulator phase, a stripe insulator phase, and a phase separation region, in agreement with the phase diagram obtained analytically in the strong coupling limit (i.e., in the absence of fermion hopping). In the intermediate interaction regime we establish a quantum anomalous Hall phase in the DMRG as evidenced by the spontaneous time-reversal symmetry breaking and the appearance of a quantized Chern number
C=1. For weak interaction we utilize the power expanded Gibbs potential method that treats
V1 and
V2 on equal footing, as well as the weak coupling renormalization group. Our analytical results reveal that not only the repulsive
V1 interaction, but also the
V2 interaction (both repulsive and attractive), can drive the quantum anomalous Hall phase. We also determine the phase boundary in the ${V}_{1}\text{\ensuremath{-}}{V}_{2}$ plane that separates the semimetal from the quantum anomalous Hall state. Finally, we show that the nematic semimetal, which was proposed for $|{V}_{2}|\ensuremath{\gg}{V}_{1}$ at weak coupling in a previous study, is absent, and the quantum anomalous Hall state is the only weak coupling instability of the spinless quadratic band touching semimetal.