Noise Correlations Measurements for extended models using tensor networks

Abstract

Spontaneously symmetry-broken (SSB) phases are locally ordered states of matter. Because of their specific ordering, their presence is usually witnessed by means of local order parameters. In this Thesis, we investigate different characterization schemes that allows one to detect spontaneously broken symmetries in cold atom experiments where single-site imaging of optical lattices is not accessible. For that, we characterize several detection methods, including time-of-flight measurements and noise correlation measurements. Using tensor network methods, we first motivate our approach on a Bose-Hubbard model, where the salient physics is be presented. Later on, we benchmark our approach on an extended Fermi-Hubbard model, where the final protocol is presented. Our numerical analysis shows that noise correlations can accurately capture the presence of spontaneously broken symmetries, thus representing an alternative and powerful strategy to characterize strongly interacting quantum matter.