Emergent Spacetime Supersymmetry at the Superconducting Critical Point of a Single Dirac Cone

It has been theoretically argued that SUSY can also spontaneously emerge in certain condensed matter systems, e.g., near the superconducting quantum critical point (QCP) of an interacting single-flavored Dirac fermion in 2+1 dimensional systems. However, whether this fascinating N=2 SUSY can emerge in microscopic lattice models in 2+1 dimensions remain unknown so far. Here, we introduce a lattice realization of a single Dirac fermion with onsite attractive Hubbard interactions that preserves both time reversal and chiral symmetries. By performing the state-of-the-art sign-problem-free quantum Monte Carlo (QMC) simulations, we show that the interacting single Dirac fermion in 2+1 dimensions features a superconducting quantum phase transition. More remarkably, we demonstrate that the N=2 space-time SUSY in 2+1D emerges at the superconducting QCP by showing that the fermions and bosons have identical anomalous dimensions 1/3 as well as various other hallmarks of emergent SUSY. To the best of our knowledge, this is the first numerical observation of emergent space-time SUSY in 2+1D systems [1].
[1] Zi-Xiang Li, Abolhassan Vaezi, Christian Mendl, and Hong Yao, to appear soon.