Data and processing tools supporting results presented in publication "Non-magnetic floating phases in frustrated Haldane chains with a single-ion anisotropy" and chapter 4 in PhD thesis "quantum criticality in frustrated Haldane chains and (doped) quantum loop models"

This dataset includes data obtained from large-scale simulations performed with the density matrix renormalization group algorithm, and the tools used to process this data. The data obtained from these simulations support our studies on the effect of a single-ion anisotropy in the bilinear–biquadratic spin-1 J1–J2 chain.We investigate the effect of a single-ion anisotropy in the bilinear–biquadratic spin-1 J1–J2 chain, focusing on the quantum phase transitions out of the trimerized phase. We uncover a rich phase diagram comprising five gapped phases and, remarkably, two critical floating phases. These incommensurate Luttinger liquid phases emerge from the proliferation of non-magnetic domains – Sz_i = 0 states and dimers – within a trimerized background and are confined to the zero-magnetization sector, while magnetic excitations remain gapped. We show that transitions between the symmetry-protected topological Haldane phase and the floating phases are governed by a composite critical line with central charge c = 2, consistent with the coexistence of magnetic Gaussian and non-magnetic critical modes. These results shed new light on the long-standing problem of the Haldane–trimerized transition.