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TT: Fachverband Tiefe Temperaturen

TT 23: Correlated Electrons – Poster I

TT 23.8: Poster

Monday, March 9, 2026, 18:00–20:00, P1

Convergence behavior of non-perturbative linked-cluster expansions at criticality — •Harald Leiser, Max Hörmann, and Kai Phillip Schmidt — Chair for Theoretical Physics V, FAU Erlangen-Nürnberg, Germany

Non-perturbative linked-cluster expansions (NLCE) provide a systematic framework for computing properties of quantum lattice models directly in the thermodynamic limit. For applying it to excited states, we use a transformation T that block-diagonalizes cluster Hamiltonians, like the Schrieffer-Wolff transformation, while satisfying cluster-additivity. In perturbative linked-cluster expansions up to order N, certain classes of transformations all yield identical and exact results at order N. However, in non-perturbative LCE this equivalence breaks down entirely, as the hierarchical structure of contributions is absent. As a result, the non-perturbative effects introduced by different transformations can produce different convergence behavior, also depending on the observable under study. Our goal is to understand how different choices of T influence the convergence behavior and what these differences reveal about the transformations themselves. Furthermore, we aim to understand the role of the transformation T in extracting quantum-critical behavior from NLCEs. For that, we analyze the energy gap of the transverse-field Ising chain at its quantum critical point, since its exact solution reduces the computational complexity to polynomial, enabling comparison up to large system sizes.

Keywords: Linked-cluster expansions; Block diagonalisation; Transverse-field Ising model; Cluster additivity