Quantum Phase Transition in Interacting Quantum Wires*

We consider the quantum phase transition of interacting electrons in a quantum wire from a one-dimensional (1D) to a quasi-1D state as a function of an external gate voltage. At weak interactions, a Lifshitz transition occurs when electrons start filling the second subband of transverse quantization. The physics in the vicinity of the transition is characterized by pronounced correlations as interactions in the second subband are effectively strong due to the diverging density of states close to the band bottom. Inter-subband interactions lead to the formation of polarons, but the nature of the transition is unchanged, i.e., one finds a Lifshitz transition of impenetrable polarons. By contrast, strongly interacting electrons form a (quasi-)1D Wigner crystal, and the transition corresponds to the linear crystal splitting into a zigzag crystal. This Ising transition in the charge sector is decoupled from the spin excitations in the system.