One-dimensional model for deconfined criticality with Z3 x Z3 symmetry

We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a Z(3) ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with Z(3) x 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 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.

Automated summary

Researchers continue to explore examples of deconfined quantum criticality in one-dimensional models, specifically studying the transition between a Z(3) ferromagnet and a valence bond solid (VBS) phase. Evidence suggests a possible second-order or weakly first-order transition, with an integrable lattice model in the parameter space indicating an extremely weak first-order transition with a long correlation length. This transition is proposed to be part of a family of deconfined quantum critical points described by renormalization group flows.