Elaborating the phase diagram of spin-1 anyonic chains
Annotatsiya
We revisit the phase diagram of spin-1 su(2)_k <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>s</mml:mi> <mml:mi>u</mml:mi> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mn>2</mml:mn> <mml:msub> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:mi>k</mml:mi> </mml:msub> </mml:mrow> </mml:math> anyonic chains, originally studied by Gils et. al. . These chains possess several integrable points, which were overlooked (or only briefly considered) so far. Exploiting integrability through a combination of algebraic techniques and exact Bethe ansatz results, we establish in particular the presence of new first order phase transitions, a new critical point described by a Z_k <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>Z</mml:mi> <mml:mi>k</mml:mi> </mml:msub> </mml:math> parafermionic CFT, and of even more phases than originally conjectured. Our results leave room for yet more progress in the understanding of spin-1 anyonic chains.