Supersymmetric waves in Bose-Fermi mixtures

Interacting Bose-Fermi mixtures possess a fermionic (super)symmetry when bosons and fermions in the mixture have equal masses, and when the interaction strengths are appropriately tuned. This symmetry is spontaneously broken in the ground state of the mixture, leading to a novel Goldstone mode with fermionic statistics and quadratic dispersion. Here we examine the effect of explicit symmetry-breaking perturbations on the Goldstone mode. When the symmetry is not exact and the system is allowed to deviate from the symmetric point, we find that the Goldstone mode acquires an energy gap. We show that the excitations manifest themselves as a nonanalyticity of the thermodynamic pressure.