Generic "Unnecessary" Quantum Critical Points with Minimal Degrees of Freedom

Abstract

We explore generic "unnecessary" quantum critical points with minimal degrees of freedom. These quantum critical points can be avoided with strong enough symmetry-allowed deformations of the Hamiltonian, but these deformations are irrelevant perturbations below certain threshold at the quantum critical point. These quantum critical points are hence unnecessary, but also unfine-tuned (generic). The previously known examples of such generic unnecessary quantum critical points involve at least eight Dirac fermions in both two and three spatial dimensions. In this work we seek for examples of generic unnecessary quantum critical points with minimal degrees of freedom. In particular, in three dimensional space, we identify two examples of such generic unnecessary quantum critical points. The first example occurs in a $3d$ interacting topological insulator, and it is described by $two$ $(3+1)d$ massless Dirac fermions in the infrared limit; the second example occurs in a $3d$ topological superconductor, and it is formally described only $one$ $(3+1)d$ massless Dirac fermion.

10 pages, 4 figures. In order to be self-contained, this preprint contains a review of our previous work arXiv:1906.07191 in section IIA

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• Dirac spin liquid as an "unnecessary" quantum critical point on square lattice antiferromagnets
• Charge pumps, boundary modes, and the necessity of unnecessary criticality
• Unnecessary quantum criticality in $SU(3)$ kagome magnets
• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice