Eight-vertex criticality in the interacting Kitaev chain

TL;DR

This paper demonstrates that the interacting Kitaev chain with pairing and repulsion exhibits an eight-vertex critical line with floating phases and emergent U(1) symmetry, confirmed through exact solutions and DMRG simulations.

Contribution

It reveals a new critical behavior in the interacting Kitaev chain, connecting it to the eight-vertex universality class and confirming the phase diagram features with numerical methods.

Findings

Critical line in the eight-vertex universality class.

Floating phases with emergent U(1) symmetry.

Agreement between Baxter's exact solution and DMRG simulations.

Abstract

We show that including pairing and repulsion into the description of 1D spinless fermions, as in the domain wall theory of commensurate melting or the interacting Kitaev chain, leads, for strong enough repulsion, to a line of critical points in the eight vertex universality class terminating floating phases with emergent U(1) symmetry. For nearest-neighbor repulsion and pairing, the variation of the critical exponents along the line that can be extracted from Baxter's exact solution of the XYZ chain at $J_x=-J_z$ is fully confirmed by extensive DMRG simulations of the entire phase diagram, and the qualitative features of the phase diagram are shown to be independent of the precise form of the interactions.