Data and data processing tools supporting results presented in chapter 7 of 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 one-dimensional doped quantum dimer and loop models designed to engineer the low-energy physics of spontaneous dimerization in antiferromagnetic Heisenberg spin chains associated with Wess-Zumino-Witten SU(2)$_{2S}$ criticality. To this end, we extend the non-magnetic Hilbert space of quantum dimer and loop models by incorporating mobile spin-$1/2$ degrees of freedom. We benchmark this framework against several paradigmatic cases. For spin-$1/2$, the doped quantum dimer model qualitatively reproduces the $J_1-J_2$ chain. By careful study of the excitation spectrum we show that its low-energy behavior is consistent with Wess-Zumino-Witten SU(2)$_1$ criticality. For spin-$1$, the model captures both the topological Haldane phase and the dimerized phase, with a transition that is either direct and first order or proceeds via an intermediate topologically non-trivial $\mathbb{Z}_2$ ordered phase bounded by Gaussian and Ising critical lines. Finally, for spin-$3/2$, the model again reproduces a Luttinger liquid with a low-energy description in agreement with SU(2)$_1$ criticality. Partially and fully dimerized phases are realized as well and are separated by a Gaussian transition of which its realization is possible through the structure of the Hilbert space. The boundary of the Luttinger liquid is governed by a first-order transition. We argue that the SU(2)$_{2S}$ critical points for $S=1$ and $S=3/2$ may be accessed through careful fine-tuning within the large parameter space of these models.