Magnetically Stabilized Order. II: Critical states and algebraically ordered nematic spin liquids in one-dimensional optical lattices

TL;DR

This paper explores quantum phase transitions in one-dimensional optical lattices of spin-one bosons, revealing critical behavior characterized by hardcore boson condensation, Luttinger liquid dynamics, and a Bethe Ansatz solution.

Contribution

It introduces a detailed analysis of critical states and algebraically ordered nematic spin liquids in 1D optical lattices, highlighting the role of hardcore interactions and Luttinger liquid parameters.

Findings

Critical behavior involves hardcore boson condensation instead of magnons.

Critical states resemble free Fermion models with Friedel oscillations.

Nematic spin liquids near critical points are described by tunable Luttinger liquid parameters.

Abstract

We investigate the Zeeman-field-driven quantum phase transitions between singlet spin liquids and algebraically ordered O(2) nematic spin liquids of spin-one bosons in one-dimensional optical lattices. We find that the critical behavior is characterized by condensation of hardcore bosons instead of ideal magnons in high dimensional lattices. Critical exponents are strongly renormalized by hardcore interactions and critical states are equivalent to the free Fermion model up to the Friedal oscillations. We also find that the algebraically ordered nematic spin liquids close to critical points are fully characterized by the Luttinger liquid dynamics with Luttinger liquid parameters magnetically tunable. The Bethe Ansatz solution has been applied to determine the critical magnetization and nematic correlations.