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We investigate the nature of the phase transition between the period-threecharge-density wave and the disordered phase of a hard-boson model proposed inthe context of cold-atom experiments. Building on a density-matrixrenormalization group algorithm that takes full advantage of the hard-bosonconstraints, we study systems with up to 9'000 sites and calculate thecorrelation length and the wave-vector of the incommensurate short-rangecorrelations with unprecedented accuracy. We provide strong numerical evidencethat there is an intermediate floating phase far enough from the integrablePotts point, while in its vicinity, our numerical data are consistent with aunique transition in the Huse-Fisher chiral universality class.

Floating phase versus chiral transition in a 1D hard-boson model