One-dimensional model for deconfined criticality with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>×</mml:mo><mml:msub><mml:mi mathvariant="double-struck">Z</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:math> symmetry
Brenden Roberts, Shenghan Jiang, Olexei I. Motrunich
Abstract
We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a ${\mathbb{Z}}_{3}$ ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with ${\mathbb{Z}}_{3}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{3}$ global symmetry. We study a model with alternating projective representations on the sites of the two sublattices, allowing the Hamiltonian to connect to an exactly solvable point having VBS order with the character of $SU(3)$-invariant singlets. Such a model does not admit a Lieb-Schultz-Mattis theorem typical of systems realizing deconfined critical points. Nevertheless, we find evidence for a direct transition from the VBS phase to a ${\mathbb{Z}}_{3}$ ferromagnet. Finite-entanglement scaling data are consistent with a second-order or weakly first-order transition. We find in our parameter space an integrable lattice model apparently describing the phase transition, with a very long, finite, correlation length of 190878 lattice spacings. Based on exact results for this model, we propose that the transition is extremely weakly first order and is part of a family of deconfined quantum critical points described by walking of renormalization group flows.