Floating Phase versus Chiral Transition in a 1D Hard-Boson Model

Abstract

We investigate the nature of the phase transition between the period-three charge-density wave and the disordered phase of a hard-boson model proposed in the context of cold-atom experiments. Building on a density-matrix renormalization group algorithm that takes full advantage of the hardboson constraints, we study systems with up to 9'000 sites and calculate the correlation length and the wave-vector of the incommensurate short-range correlations with unprecedented accuracy. We provide strong numerical evidence that there is an intermediate floating phase far enough from the integrable Potts point, while in its vicinity, our numerical data are consistent with a unique transition in the Huse-Fisher chiral universality class. arXiv:1808.08990v2 [cond-mat.str-el] 1 Nov 2018

Diagnosing Potts criticality and two-stage melting in one-dimensional hard-core boson models

“…As discussed above, all entanglement-related quantities signal a single second-order phase transition. This implies that the transition between the IC and disordered phase shall belong to the BKT universality class, in agreement with field theoretical insights 17,21 .…”

“…As already noted in Ref. 21 and further discussed below, the peculiar way order is realized in the system causes extremely strong finite-size effects, especially when OBCs are applied. This poses challenges for tensor-network based techniques, which usually rely on these boundary conditions, since the computational effort must be increased in order to access larger system sizes.…”

“…1). In particular, there are two ordered phases with Z 2 and Z 3 order 17 and a disordered phase in which long-range correlations can be incommensurate with the lattice spacing 21 . The transition separating the period-two ordered phase from the disordered one is well understood: one switches from first to second order at a tricritical point, the second-order line belonging to the Ising model universality class 24 .…”

“…The phase diagram hosts an integrable line, which crosses the boundary between the Z 3 -ordered and disordered phases at a critical point belonging to the Potts universality class 24,25 . Below it, the phase transition is still continuous, but Lorentz invariance is broken at low energy by an irrelevant chiral perturbation which changes the critical exponents 21,26 . Eventually, a gapless phase opens on the line and the order-disorder transition becomes a Luttinger liquid phase 24,27 with incommensurate long-range correlations 17,21 .…”

“…In principle, the transition may remain in the Potts universality class; however, this scenario is unlikely as it would require fine-tuning. Recently, numerical evidence has been provided both in favor of a continuous phase transition surviving on the whole line 20 and in favor of a gapless phase opening at a point above the Potts one 21 , while simulations on small system sizes are compatible with Potts universality extending up to infinite NNN repulsion 19 .…”