Topology plays a cardinal role in explaining phases and quantum phase transitions beyond the Landau-Ginzburg-Wilson paradigm. In this Letter, we formulate a set of models of Dirac fermions in $2+1$ dimensions with $\mathrm{SU}\left(N\right)\times \mathrm{SU}\left(2\right)\times \mathrm{U}\left(1\right)$ symmetry that have the potential to host critical points described by field theories with topological terms. For $N=2$ it shows a rich phase diagram containing semimetallic, quantum spin Hall insulating, Kekulé valence bond solid, and $s$-wave superconducting phases, and features multiple Landau-Ginzburg-Wilson phase transitions driven by interaction strength. At $N=1$ a deconfined quantum critical point is observed. At $N=2$ one expects the critical theory to correspond to a level 2 Wess-Zumino-Witten theory in $2+1$ dimensions. Here, the numerical results however show a strong first-order transition. Another transition can be governed by a topological $\theta$ term which is rendered irrelevant for even values of $N$, thus leading to Landau-Ginzburg-Wilson behavior.

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• Quantum criticality
• Quantum phase transitions
• Superconductor-insulator transition
• Symmetry protected topological states
• Valence bond solid
• Quantum Monte Carlo