The problem of continuous quantum phase transitions in metals involves critical bosons coupled to a Fermi surface. We solve the theory in the limit of a large number, $N_B$, of bosonic flavors, where the bosons transform in the adjoint representation (a matrix representation), while the fermions are in the fundamental representation (a vector representation) of a global $SU\left(N_B\right)$ flavor symmetry group. The leading large $N_B$ solution corresponds to a non-Fermi liquid coupled to Wilson-Fisher bosons. In a certain energy range, the fermion velocity vanishes—resulting in the destruction of the Fermi surface. Subleading $1/N_B$ corrections correspond to a qualitatively different form of Landau damping of the bosonic critical fluctuations. We discuss the model in $d=3-\epsilon$ but because of the additional control afforded by large $N_B$, our results are valid down to $d=2$. In the limit $\epsilon \ll 1$, the large $N_B$ solution is consistent with the renormalization group analysis of Fitzpatrick et al. [Phys. Rev. B 88, 125116 (2013)].

• Received 13 January 2014
• Revised 30 March 2014

DOI:https://doi.org/10.1103/PhysRevB.89.165114