Title: Can supersymmetry emerge at a quantum critical point?,
Abstract: Supersymmetry plays an important role in superstring theory and particle
physics, but has never been observed in experiments. At certain quantum
critical points of condensed matter systems, the fermionic excitations are
gapless due to the special electronic structure whereas the bosonic order
parameter is automatically gapless, offering a promising platform to realize
emergent supersymmetry by tuning a single parameter. Here, we study under what
circumstances can supersymmetry emerge in a quantum critical system. We
demonstrate that the Yukawa-type coupling between the gapless fermion and boson
may induce a number of highly nonlocal self-interacting terms in the effective
field theory of the boson. Only when such terms do not exist or are irrelevant,
could supersymmetry have the chance to be dynamically generated at low
energies. This strong constraint provides an important guidance for the
exploration of emergent supersymmetry in various condensed matter systems, and
also should be carefully considered in the study of quantum critical behaviors.