Gapless Phase in the XYZ Spin-1/2 Chain in a Magnetic Field and the Quantum ANNNI Chain

TL;DR

This paper investigates the XYZ spin-1/2 chain in a magnetic field, revealing a critical line of gapless states due to a non-trivial fixed point, and explains the nature of the floating phase in the quantum ANNNI chain.

Contribution

It identifies a line of critical points in the XYZ chain using bosonization and RG analysis, elucidating the gapless phase structure and its relation to the quantum ANNNI model.

Findings

Existence of a critical line with gapless excitations

Identification of a non-trivial fixed point in the phase diagram

Explanation of the floating phase as a line of criticality

Abstract

We study the XYZ spin-1/2 chain placed in a magnetic field pointing along the x-axis. We use bosonization and a renormalization group analysis to show that the model has a non-trivial fixed point at a certain value of the XY anisotropy a and the magnetic field h. Hence, there is a line of critical points in the plane (a,h) on which the system is gapless, even though the Hamiltonian has no continuous symmetry. The quantum critical line separates a gapped commensurate phase from a gapped incommensurate phase. Our study explains why the floating phase of the axial next-nearest neighbor Ising (ANNNI) chain in a transverse magnetic field is only a line, as shown by recent numerical studies.