Particle-Hole Symmetry and the Bose Glass to Superfluid Transition

The generic Hamiltonian describing the zero temperature transition between the insulating Bose glass phase and the superfluid phase lacks particle-hole symmetry, but a statistical version of this symmetry is believed to be restored at the critical point. We show that the renormalization group relevance of particle-hole asymmetry may be explored in a controlled fashion only for small time dimensions, ${\epsilon }_{\tau }\ll 1$, where we find a stable particle-hole asymmetric and an unstable particle-hole symmetric fixed point, but we provide evidence that the two merge for some finite ${\epsilon }_{\tau }\approx \frac{2}{3}$, which tends to confirm symmetry restoration at the physical ${\epsilon }_{\tau }=1\mathrm{}$.