Dimerization in a quantum spin chain

Vienna Probability Seminar

This talk concerns the phenomenon of symmetry-breaking in statistical physics, particularly "dimerization" where the broken symmetry is that of translation-invariance. After reviewing the main ideas of symmetry-breaking in statistical physics, I will describe a quantum spin system in one dimension where we prove that dimerization occurs. The model considered here can be seen as a perturbation of a model for which Aizenman, Duminil-Copin and Warzel recently proved dimerization for all spins larger than 1/2. In our case, we prove dimerization for large enough spin. The proof uses a probabilistic representation in terms of a collection of random loops and a cluster-expansion. Based on the paper arXiv:2101.11464 which is joint work with Peter Mühlbacher, Bruno Nachtergaele and Daniel Ueltschi.