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

2010/12/31 by Salvatore R. Manmana, Andreas M. Läuchli, Fabian H. L. Essler +2
Mathematics · Physics and Astronomy · #Bethe ansatz #Bilinear interpolation #Condensed matter physics #Integrable system #Ising model #Luttinger liquid #Mathematical physics #Mathematics #Phase (matter) #Phase diagram #Phase transition #Physics #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Renormalization group #cond-mat.str-el

paper · pdf · doi:10.1103/physrevb.83.184433

published as Phys. Rev. B 83, 184433 (2011) · revised version, as published in PRB

arxiv created 2011/05/31 · openalex publication_date 2011/05/31 · arxiv updated 2011/06/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/06

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 quasicondensate 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.

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