Phase diagram and continuous pair-unbinding transition of the bilinear-biquadratic S=1 Heisenberg chain in a magnetic field

TL;DR

This paper studies the phase diagram of the S=1 Heisenberg chain with bilinear and biquadratic interactions in a magnetic field, revealing a continuous pair unbinding transition and characterizing the nature of various Luttinger liquid phases.

Contribution

It provides a detailed analysis of the phase transitions and critical behavior, including the identification of the Ising universality class for the pair unbinding transition.

Findings

Identification of a magnetized ferroquadrupolar Luttinger liquid phase.

Observation of a continuous pair unbinding transition with Ising universality.

Confirmation that the partially polarized phase is a two-component Luttinger liquid.

Abstract

We investigate the properties of the Heisenberg S=1 chain with bilinear and biquadratic interactions in a magnetic field using the Density Matrix Renormalization Group, Bethe ansatz and field theoretical considerations. In a large region of the parameter space, we identify a magnetized ferroquadrupolar Luttinger liquid consisting of a quasi-condensate of bound magnon pairs. This liquid undergoes a continuous pair unbinding transition to a more conventional Luttinger liquid region obtained by polarizing the system above the Haldane gap region. This pair unbinding transition is shown to be in the Ising universality class on top of a Luttinger liquid, leading to an effective central charge 3/2. We also revisit the nature of the partially polarized Luttinger liquid around and above the Uimin-Lai-Sutherland point. Our results confirm that this is a two-component liquid and rule out the formation of a single-component vector chiral phase.