Exact solution to the Haldane-BCS-Hubbard model along the symmetric lines: Interaction-induced topological phase transition

Abstract

We propose a Haldane-BCS-Hubbard model on a honeycomb lattice, which is composed of two copies of the Haldane model of the quantum anomalous Hall effect, an equal-spin pairing term and an onsite Hubbard interaction term. For any interaction strength, this model is exactly solvable along the symmetric line where the hopping and pairing amplitudes are equal to each other. The ground state of the Haldane-BCS-Hubbard model is a topological superconducting state at weak interaction with two chiral Majorana edge states. A strong interaction drives the system across a topological quantum phase transition to a topologically trivial superconductor. A Z2 symmetry of the Hamiltonian, which is a composition of the bond-centered inversion and a gauge transformation, is spontaneously broken by the interaction, resulting a finite antiferromagnetic order in the ydirection.

Phase Diagram of the BCS–Hubbard Model in a Magnetic Field

“…An extension of this BCS-Hubbard model was introduced by Ezawa [22] to include a Kane-Mele spin-orbit coupling term on the honeycomb lattice. A topological superconducting state was found in the Haldane-BCS-Hubbard model on a honeycomb lattice by Miao et al [23] In this Letter, we generalize the BCS-Hubbard model to include (a) a spin flip hopping term, (b) a p-wave pairing term by two electrons with opposite spins, and (c) an external magnetic field, and show that this model is exactly solvable along the symmetric lines where the hopping integrals become equal to the corresponding pairing amplitudes. This generalization broadens the range of the integrability of the BCS-Hubbard model and enriches its phase diagram.…”

Localization of Electronic States in Hybrid Nano-Ribbons in the Non-Perturbative Regime

“…As described in [5][6][7], for example, when ∆ has the same magnitude as the hopping parameter t, the onsite interaction term becomes quadratic in the number of creation and annihilation operators and therefore the spectrum of the system can be obtained by direct diagonalization. We repeat the derivation for our system here.…”

“…Here we perform quantum Monte Carlo (QMC) simulations for various values of the onsite coupling U that include the strongly interacting regime. In the second case we consider the so-called symmetric line limit [5][6][7], where we introduce a nearest neighbor superconducting pairing term ∆ to the Hubbard model but with equal weight as the hopping term t. In this limit the single-particle spectrum and wavefunctions, when expressed in a Majorana basis, can be determined for any value of the Hubbard onsite interaction U . In both cases we observe that the energy of the localized state is no longer depends strongly on the coupling U .…”

Exact Solutions of Topological Superconductor Model with Hubbard Interactions

“…Although its original form is a spin model, if one rewrite the Kitaev model in terms of Majorana fermions, then it is evident that there are infinite many conserved quantities, which makes this model exact solvable. More recently, this line of developments has been revived and a large class of exact solvable BCS-Hubbard models have been proposed in a series of works [14][15][16][17]. These types of models are studied under the name of the Falicov-Kimball model many years ago.…”