Observation of Emergent Spacetime Supersymmetry at Superconducting Quantum Criticality

TL;DR

This paper reports the first numerical evidence of emergent 2+1D spacetime supersymmetry at a superconducting quantum critical point in a lattice model of a Dirac fermion, with potential experimental implications.

Contribution

It introduces a lattice model with attractive interactions that exhibits emergent spacetime SUSY at a quantum critical point, confirmed by sign-problem-free quantum Monte Carlo simulations.

Findings

Emergent ${ m extbf{N}}$=2 spacetime SUSY at the critical point

Fermions and bosons have identical anomalous dimensions of 1/3

Potential experimental signatures on topological insulator surfaces

Abstract

No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. Moreover, whether spacetime SUSY in 2+1 and higher dimensions can occur or emerge in generic microscopic models remains open. Here, we introduce a lattice realization of a \textit{single} Dirac fermion with attractive Hubbard interactions that preserves both time-reversal and chiral symmetries. By performing numerically-exact sign-problem-free determinant quantum Monte Carlo simulations, we show that the interacting single Dirac fermion in 2+1 dimensions features a superconducting quantum critical point (QCP). More remarkably, we demonstrate that the ${\mathcal N}$=2 spacetime SUSY in 2+1D emerges at the superconducting QCP by showing that the fermions and bosons have \textit{identical} anomalous dimensions 1/3, a hallmark of the emergent SUSY. To the best of our knowledge, this is the first observation of emergent 2+1D spacetime SUSY in quantum microscopic models. We further show some experimental signatures which can be measured to test such emergent SUSY in candidate systems such as the surface of 3D topological insulators.