Intertwined Orders, Quantum Criticality and Skyrmions in Tunable Topological Bands

TL;DR

This work investigates intertwined orders, skyrmions, and quantum criticality in tunable topological Chern bands at filling $\nu=2$. Using determinant quantum Monte Carlo alongside Hartree-Fock and Bethe-Salpeter analyses, the authors show a robust CAF insulating phase that gives rise to spin-skyrmion–driven superconductivity upon doping, and they formulate an $SO(5)$-symmetric low-energy theory with a level-1 WZW term to describe the critical point. Finite-size scaling of quantum phase transitions as a function of interaction anisotropy and bandwidth suggests a direct, continuous CAF–SC transition with emergent $SO(5)$ symmetry, consistent with deconfined quantum criticality, albeit with exponents that differ from conventional 3D universality classes and potential pseudo-critical behavior due to intricate RG flows. The results illuminate how topology, strong interactions, and nonperturbative fluctuations conspire to stabilize exotic excitations and unconventional criticality in topological bands, with implications for moiré materials and engineered quantum matter. Overall, the paper provides a coherent nonperturbative and field-theoretic framework linking skyrmions, superconductivity, and deconfined criticality 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.

Figures (10)

• Figure 1: (a) Schematics of band structures for a specific high-symmetry cut in the Brillouin zone for $\mathcal{F}\equiv W/E_{\textnormal{gap}} = 0.01$, where blue (red) curve denotes spinful bands with $\tau=+$ ($\tau=-$). The Chern number $C=\tau$. (Double) Wavy line denotes (anti-)ferromagnetic interaction projected to the active Hilbert space. (b) Schematics of the correlated CAF insulator. Color scheme and notations for interaction vertices are the same as in panel (a). (c) Schematics of the doped skyrmions on top of the CAF insulator.
• Figure 2: (a)-(b) Excitation spectrum obtained from Hartree-Fock calculation (orange dots) at $|J_\textnormal{H}|/J_\textnormal{A}=0.5$ for (a) quasi-particle and for (b) magnon in the CAF phase. Diffuse blue/violet curves denote the spectral function $A_\lambda({\boldsymbol{k}},\omega)$ obtained from stochastic analytical continuation in PQMC simulation, where $\lambda\equiv \textnormal{electron, CAF}$. (c)-(d) Excitation spectrum for composite charged spin-polaron obtained from Hartree-Fock calculation at (c) $J_\textnormal{A}=0$ and at (d) $|J_\textnormal{H}|/J_\textnormal{A}=0.5$. Blue dots denote spin-3/2 spin-polaron continuum; Black crosses denote the spin-1/2 spin-polaron excitation; red lines denote the electronic quasi-particle excitation spectrum, serving as a guide to eye for comparison.
• Figure 3: Feynman diagrams for CAF collective mode (a) propagator, (b) Bethe-Salpeter Kernel. Black (red) solid lines with arrow denote the Green's function of electronic quasi-particle. Wavy lines and double wavy lines denote the interaction vertex from intra-valley Hunds coupling ($\sim J_\textnormal{H}$) and inter-valley anti-ferromagnetic coupling ($\sim J_\textnormal{A}$), respectively.
• Figure 4: Feynman diagrams for composite charged excitations showing the (a) propagator, and (b) Bethe-Salpeter Kernel. Dashed lines denote identity in the corresponding matrix entries. Color convention is the same as in Fig. \ref{['fig::feyn1']}.
• Figure 5: A schematic representation of the flatness ratio and interaction-anisotropy tuned quantum phase transition(s). Dotted line denotes the parameter set scanned in PQMC. Red and blue arrows denote the vicinity of the transitions observed in PQMC.