Emergent Spacetime Supersymmetry at 2D Fractionalized Quantum Criticality

While experimental evidence for spacetime supersymmetry (SUSY) in particle physics remains elusive, condensed matter systems offer a promising arena for its emergence at quantum critical points (QCPs). Although there have been a variety of proposals for emergent SUSY at symmetry-breaking QCPs, the emergence of SUSY at fractionalized QCPs remains largely unexplored. Here, we demonstrate emergent spacetime SUSY at a fractionalized QCP in the Kitaev honeycomb model with Su-Schrieffer-Heeger (SSH) spin-phonon coupling. Specifically, through numerical computations and analytical analysis, we show that the anisotropic SSH-Kitaev model hosts a fractionalized QCP between a Dirac spin liquid and an incommensurate or commensurate valence-bond-solid phase coexisting with Z_{2} topological order. A low-energy field theory incorporating phonon quantum fluctuations reveals that this fractionalized QCP features an emergent N=2 spacetime SUSY. We further discuss their universal experimental signatures in thermal transport and viscosity, highlighting the concrete lattice realization of emergent SUSY at a fractionalized QCP in 2D.