Emergent Lorentz Symmetry with Vanishing Velocity in a Critical Two-Subband Quantum Wire

We consider a quantum wire with two subbands of spin-polarized electrons in the presence of strong interactions. We focus on the quantum phase transition when the second subband starts to get filled as a function of gate voltage. Performing a one-loop renormalization group analysis of the effective Hamiltonian, we identify the critical fixed-point theory as a conformal field theory having an enhanced SU(2) symmetry and central charge 3/2. While the fixed point is Lorentz invariant, the effective speed of light nevertheless vanishes at low energies due to marginally irrelevant operators leading to a diverging critical specific heat coefficient.