Emergent Lorentz Symmetry with Vanishing Velocity in a Critical
Two-Subband Quantum Wire
 
Mattias Sitte
University of Cologne
 

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, eg., a diverging critical  specific heat coefficient.  

REFERENCE: M. Sitte, A. Rosch, J. S. Meyer, K. A. Matveev, and M. Garst Phys. Rev. Lett. 102, 176404 (2009)