A strongly coupled zig-zag transition

TL;DR

This paper explores a generalized model of the zig-zag transition in 1D quantum wires, analyzing its complex phase structure and RG flows using field theory and AdS/CFT methods, including cases with multiple Majorana fermions.

Contribution

It extends previous models by replacing the Majorana fermion with a general CFT, revealing new qualitative features and analyzing the phase structure with advanced theoretical techniques.

Findings

Rich phase structure with new qualitative features

RG flow analysis shows velocity quenching in subsectors

AdS/CFT captures subleading effects in large central charge limit

Abstract

The zig-zag symmetry transition is a phase transition in 1D quantum wires, in which a Wigner lattice of electrons transitions to two staggered lattices. Previous studies model this transition as a Luttinger liquid coupled to a Majorana fermion. The model exhibits interesting RG flows, involving quenching of velocities in subsectors of the theory. We suggest an extension of the model which replaces the Majorana fermion by a more general CFT; this includes an experimentally realizable case with two Majorana fermions. We analyse the RG flow both in field theory and using AdS/CFT techniques in the large central charge limit of the CFT. The model has a rich phase structure with new qualitative features, already in the two Majorana fermion case. The AdS/CFT calculation involves considering back reaction in space-time to capture subleading effects.