Topological phase transitions and universality in the Haldane-Hubbard model

Abstract

We study the Haldane-Hubbard model by exact Renormalization Group techniques. We construct the topological phase diagram, for weak interactions. We predict that many-body interactions induce a shift of the transition line. The presence of new intermediate phases, absent in the non interacting case, is rigorously excluded at weak coupling. Despite the nontrivial renormalization of the wave function and of the Fermi velocity, the conductivity is universal: at the renormalized critical line, both the discontinuity of the transverse conductivity and the longitudinal conductivity do not depend on the interaction, thanks to remarkable cancellations due to lattice Ward Identities.

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Cited by in corpus (14)

• Interactions remove the quantization of the chiral photocurrent at Weyl points
• Spin Hall insulators beyond the Helical Luttinger model
• Quantization of the interacting Hall conductivity in the critical regime
• Universal edge transport in interacting Hall systems
• Multi-Channel Luttinger Liquids at the Edge of Quantum Hall Systems
• Absence of quantization in the circular photogalvanic effect in disordered chiral Weyl semimetals
• Quantum cluster approach to the topological invariants in correlated Chern insulators
• A supersymmetric hierarchical model for weakly disordered $3d$ semimetals
• Adiabatic Evolution of Low-Temperature Many-Body Systems
• Emergence of charge density wave and superconducting phase transitions through Lorentz-invariant interactions in the Haldane-Hubbard model
• Mapping Chern numbers in quasi-periodic interacting spin chains
• Order, disorder and phase transitions in quantum many body systems
• Spin transport and lack of quantisation for time-reversal symmetric insulators on the honeycomb structure
• Anomaly non-renormalization in interacting Weyl semimetals