Intertwined Orders, Quantum Criticality and Skyrmions in Tunable Topological Bands

Abstract

Skyrmions are emergent many-body excitations that lie at the heart of both multi-component quantum Hall-like systems and deconfined quantum criticality. In a companion article (X. Wang et al., arXiv:2507.22971), we studied a microscopic time-reversal symmetric model of tunable interacting Chern bands using numerically exact determinant quantum Monte Carlo calculations, and presented evidence for the emergence of robust skyrmion excitations. These charged excitations emerge in the vicinity of a many-body insulator at a commensurate filling of the Chern bands, and lead to the onset of superconductivity when doped away from the insulating phase. Here, we present quantum Monte-Carlo results and a complementary field-theoretical analysis for the quantum phase transition(s) that arise between the intertwined phases as a function of two distinct tuning parameters. Our numerical results are consistent with a single continuous quantum phase transition between an insulating Chern antiferromagnet and a fully gapped superconductor, with an emergent SO(5) symmetry at the putative critical point, highly suggestive of deconfined quantum (pseudo-)criticality. We also present a detailed comparison between the momentum-resolved spectral functions associated with the neutral collective modes, single electron and composite spin-polaron excitations obtained using a combination of Monte-Carlo computations and a Bethe-Salpeter analysis built on top of the self-consistent Hartree-Fock calculation. We end with a brief outlook on some of the interesting open problems.