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We show the existence of a stable algebraic spin liquid (ASL) phase in a Hubbard model defined on a honeycomb lattice with spin-dependent hopping that breaks time-reversal symmetry. The effective spin model is the Kitaev model for large on-site repulsion. The gaplessness of the emergent Majorana fermions is protected by the time-reversal invariance of this model. We prove that the effective spin model is time-reversal invariant in the entire Mott phase, thus ensuring the stability of the ASL. The model can be physically realized in cold atom systems, and we propose experimental signals of the ASL.

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The semimetal to antiferromagnet quantum phase transition of the Hubbard model on the honeycomb lattice has come to the forefront in the context of the proposal that a semimetal to spin liquid transition can occur before the transition to the antiferromagnetic phase. To study the semimetal to antiferromagnet transition, we generalize the two-particle self-consistent (TPSC) approach to the honeycomb lattice (a structure that can be realized in graphene for example). We show that the critical interaction strength where the transition occurs is U c /t = 3.79 ± 0.01, quite close to the value U c /t = 3.869 ± 0.013 reported using large-scale quantum Monte Carlo simulations. This reinforces the conclusion that the semimetal to spin-liquid transition is preempted by the transition to the antiferromagnet. Since TPSC satisfies the Mermin-Wagner theorem, we find temperature-dependent results for the antiferromagnetic and ferromagnetic correlation lengths as well as the dependence of double occupancy and of the renormalized spin and charge interactions on the bare interaction strength. We also estimate the value of the crossover temperature to the renormalized classical regime as a function of interaction strength.

We investigate the role of disorder in a two-dimensional semi-Dirac material characterized by a linear dispersion in one direction and a parabolic dispersion in the orthogonal direction. Using the self-consistent Born approximation, we show that disorder can drive a topological Lifshitz transition from an insulator to a semi metal, as it generates a momentum-independent off-diagonal contribution to the self-energy. Breaking time-reversal symmetry enriches the topological phase diagram with three distinct regimes-single-node trivial, two-node trivial, and two-node Chern. We find that disorder can drive topological transitions from both the single-and two-node trivial to the two-node Chern regime. We further analyze these transitions in an appropriate tight-binding Hamiltonian of an anisotropic hexagonal lattice by calculating the real-space Chern number. Additionally, we compute the disorder-averaged entanglement entropy which signals both the topological Lifshitz and Chern transition as a function of the anisotropy of the hexagonal lattice. Finally, we discuss experimental aspects of our results.