Phase diagram of the interacting Haldane model with spin-dependent sublattice potentials

Abstract

Using the exact-diagonalization (ED) and mean-field (MF) approaches, we investigate the ground-state phase diagram of the interacting Haldane model on the honeycomb lattice, incorporating spin-dependent sublattice potentials ${\Delta }_{\sigma ,\alpha }$. Here $\alpha =\text{A}$,$\text{B}$ and $\sigma =\uparrow$,$\downarrow$ denote the sublattice and spin components, respectively. Setting ${\Delta }_{\sigma ,\text{A}}=+\Delta$ ($-\Delta$) and ${\Delta }_{\sigma ,\text{B}}$$=-\Delta$ ($+\Delta$) for $\sigma =\uparrow$ ($\downarrow$) results in the system favoring a spin ordered state. Conversely, introducing the nearest-neighbor Coulomb interaction can induce charge ordering in the system. Due to the competition between these factors, we observe that in both ED and MF approaches, an exotic state with Chern number $C=1$ survives amidst two locally ordered phases and a topologically ordered phase with $C=2$. In the ED method, various properties, such as the fidelity metric, the excitation gap and the structure factors, are employed to identify critical points. In the MF method, using a sufficiently large lattice size, we define the local order parameters and band gaps to characterize the phase transitions. The interacting Haldane model and the spin-dependent lattice potential may be experimentally realized in an ultracold atom gas, providing a potential means to detect this intriguing state.

arXiv comment8 pages, 8 figures

References in corpus (33)

• Topological Insulators
• Topological insulators and superconductors
• Classification of topological insulators and superconductors in three spatial dimensions
• Classification of topological quantum matter with symmetries
• Experimental realisation of the topological Haldane model
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• The (High Quality) Topological Materials In The World
• Catalogue of Topological Electronic Materials
• Ground state overlap and quantum phase transitions
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Topological classification of crystalline insulators through band structure combinatorics
• Fermi-Hubbard physics with atoms in an optical lattice
• Quantum critical scaling of the geometric tensors
• Coherent transport of neutral atoms in spin-dependent optical lattice potentials
• Interacting topological insulators: a review
• Correlation effects in two-dimensional topological insulators
• Interaction effects and quantum phase transitions in topological insulators
• Creating State-Dependent Lattices for Ultracold Fermions by Magnetic Gradient Modulation
• Topological phase transitions in the repulsively interacting Haldane-Hubbard model
• Topological Phase Transitions for Interacting Finite Systems
• Microwave Control of Atomic Motion in Optical Lattices
• Coupling-Matrix Approach to the Chern Number Calculation in Disordered Systems
• Topological antiferromagnetic phase in a correlated Bernevig-Hughes-Zhang model
• Antiferromagnetic Chern insulators in non-centrosymmetric systems
• Phase diagram topology of the Haldane-Hubbard-Coulomb model
• Interplay of local order and topology in the extended Haldane-Hubbard model
• Antiferromagnetic topological insulator state in the correlated Bernevig-Hughes-Zhang model
• Statistical Analysis of the Chern Number in the Interacting Haldane-Hubbard Model
• Phase transitions in the Haldane-Hubbard model
• Spontaneous symmetry breaking of an interacting Chern insulator on a topological square lattice
• Lattice symmetry and emergence of antiferromagnetic quantum Hall states
• Topological Anderson insulating phases in the interacting Haldane model
• Phase transitions in the Haldane-Hubbard model with ionic potentials

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