Hierarchy of correlations: Application to Green's functions and interacting topological phases

Abstract

We study the many-body physics of different quantum systems using a hierarchy of correlations, which corresponds to a generalization of the $1/\mathcal{Z}$ hierarchy. The decoupling scheme obtained from this hierarchy is adapted to calculate double-time Green's functions, and due to its non-perturbative nature, we describe quantum phase transition and topological features characteristic of strongly correlated phases. As concrete examples we consider spinless fermions in a dimers chain and in a honeycomb lattice. We present analytical results which are valid for any dimension and can be generalized to different types of interactions (e.g., long range interactions), which allows us to shed light on the effect of quantum correlations in a very systematic way. Furthermore, we show that this approach provides an efficient framework for the calculation of topological invariants in interacting systems.

14 pages,9 figures

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Cited by in corpus (5)

• Topological invariants for the Haldane phase of interacting SSH chains -- a functional RG approach
• Topology detection in cavity QED
• Transport signatures in topological systems coupled to AC fields
• Linear response theory for cavity QED materials at arbitrary light-matter coupling strengths
• Hierarchy of correlations for the Ising model in the Majorana representation