Phase transitions in the Haldane-Hubbard model

Abstract

The Haldane-Hubbard model is a prime example of the combined effects of band topology and electronic interaction. We revisit its spinful phase diagram at half-filling as a consensus on the presence of SU($2$) symmetry is currently lacking. To start, we utilize the Hartree-Fock mean-field method, which offers a direct understanding of symmetry breaking through the effective mass term that can acquire spin dependence. Our results, in agreement with previous studies, provide an instructive insight into the regime where the Chern number $C=1$, with only one spin species remaining topological. Besides that, we numerically study the phase diagram of the Haldane-Hubbard model via a large-scale infinite-density matrix renormalization group (iDMRG) method. The phase boundaries are determined by the Chern number and the correlation lengths obtained from the transfer-matrix spectrum. Unlike previous studies, the iDMRG method investigates the Haldane-Hubbard model on a thin and infinitely long cylinder and examines scenarios consistent with the two-dimensional thermodynamic limit. Here, the phase diagram we obtained qualitatively goes beyond the Hartree-Fock scope, particularly in the $C=1$ region, and serves as a quantitative benchmark for further theoretical and experimental investigations.

12 pages, 9 figures

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• The density-matrix renormalization group in the age of matrix product states
• Ordering of magnetic impurities and tunable electronic properties of topological insulators
• Transfer Matrices and Excitations with Matrix Product States
• Topological antiferromagnetic phase in a correlated Bernevig-Hughes-Zhang model
• Kane-Mele-Hubbard model on the $\pi$-flux honeycomb lattice

Cited by in corpus (12)

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• Phase diagram of the interacting Haldane model with spin-dependent sublattice potentials
• The odd-parity altermagnetism: A spin group study
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• Competition between dimerization and vector chirality in the spin-$3/2$ $J_1$-$J_2$ Heisenberg chain with uniaxial single-ion anisotropy
• Topological charge excitations and Green's function zeros in paramagnetic Mott insulators
• Antiferromagnetic topological insulators in heavy-fermion systems
• From explicit to spontaneous charge order and the fate of antiferromagnetic quantum Hall state
• Impurity-induced Mott ring states and Mott zeros ring states in the Hubbard operator formalism
• Real-space topology and charge order in the Haldane-Holstein Model
• High-Temperature Quantum Anomalous Hall Effect in Buckled Honeycomb Antiferromagnets
• The antiferromagnetic Chern insulator phase in the Kane-Mele-Hubbard model