Gapless to gapless phase transitions in quantum spin chains

TL;DR

This paper studies gapless to gapless phase transitions in quantum spin chains with bilinear-biquadratic interactions under magnetic fields, revealing multiple soft modes and phase changes at critical points through spectral analysis.

Contribution

It uncovers the mechanism of gapless to gapless transitions in the ULS model and compares it with the gapped AKLT model, highlighting universality in the BLBQ family.

Findings

Identification of two soft points at zero field and their bifurcation with increasing field.

Discovery of a single soft point at $q=\pi$ at the critical field $h_{c1}$.

Observation of a transition to a fully polarized phase at $h_{c2}=4$.

Abstract

We investigate spin chains with bilinear-biquadratic (BLBQ) spin interactions as a function of an applied magnetic field $h$. At the Uimin-Lai-Sutherland (ULS) critical point we find a gapless to gapless transition revealed by the dynamical structure factor $S(q,\omega)$ as a function of $h$. At $h=0$, the envelope of the lowest energy excitations goes soft at {\it two points} $q_1=2\pi/3$ and $q_2=4\pi/3$, dubbed the phase A. With increasing field, the spectral peaks at each of the gapless points bifurcate, making in total {\it four} soft modes, and combine to form a new set of excitations that soften at a {\it single} point $q=\pi$ at $h_{c1}\approx 0.94$. Beyond $h_{c1}$ the system enters another gapless B-phase until the transition at $h_{c2}=4$ to the fully polarized phase. We compare the ULS model results with those for the AKLT model as a representative of gapped Haldane phase. We explain the mechanism of the gapless to gapless transition in the ULS model using its conserved charges and a spinon band picture. We also discuss the universality of central charges of the BLBQ family of models subjected to a magnetic field.