{
"id": "2010.07917",
"version": "v1",
"published": "2020-10-15T17:50:59.000Z",
"updated": "2020-10-15T17:50:59.000Z",
"title": "One-dimensional model for deconfined criticality with $\\mathbb{Z}_3 \\times \\mathbb{Z}_3$ symmetry",
"authors": [
"Brenden Roberts",
"Shenghan Jiang",
"Olexei I. Motrunich"
],
"comment": "19+7 pages, 10 figures, 1 table",
"categories": [
"cond-mat.str-el",
"cond-mat.stat-mech"
],
"abstract": "We continue recent efforts to discover examples of deconfined quantum criticality in one-dimensional models. In this work we investigate the transition between a $\\mathbb{Z}_3$ ferromagnet and a phase with valence bond solid (VBS) order in a spin chain with $\\mathbb{Z}_3\\times\\mathbb{Z}_3$ 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 $\\mathbb{Z}_3$ 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 DQCP described by walking of renormalization group flows.",
"revisions": [
{
"version": "v1",
"updated": "2020-10-15T17:50:59.000Z"
}
],
"analyses": {
"keywords": [
"one-dimensional model",
"deconfined criticality",
"transition",
"renormalization group flows",
"valence bond solid"
],
"note": {
"typesetting": "TeX",
"pages": 7,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}