Emergent Lorentz symmetry with vanishing velocity in a critical two-subband quantum wire

TL;DR

This paper analyzes a critical quantum phase transition in a two-subband quantum wire, revealing emergent Lorentz symmetry with a vanishing effective velocity at low energies, and characterizes the fixed point as a conformal field theory with enhanced symmetry.

Contribution

It identifies a novel critical fixed point with SU(2) symmetry and zero velocity, providing a detailed RG analysis of the phase transition in a strongly interacting quantum wire.

Findings

Fixed point has SU(2) symmetry and central charge 3/2

Lorentz invariance emerges at the critical point

Effective velocity vanishes due to marginally irrelevant operators

Abstract

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 (RG) 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.