A generalized perspective on non-perturbative linked-cluster expansions
1 Lehrstuhl für Theoretische Physik I, TU Dortmund - Otto-Hahn-Straße 4, D-44221 Dortmund, Germany
2 Laboratoire de Physique Théorique, CNRS UMR 5152, Université Paul Sabatier - F-31062 Toulouse, France
Received: 4 March 2015
Accepted: 10 April 2015
We identify a fundamental challenge for any non-perturbative approach based on finite clusters resulting from the reduced symmetry on graphs, most importantly the breaking of translational symmetry, when targeting the properties of excited states. This can be traced back to the appearance of intruder states in the low-energy spectrum, which represent a major obstacle in quasi-degenerate perturbation theory. Here a generalized notion of cluster additivity is introduced, which is used to formulate an optimized scheme of graph-based continuous unitary transformations allowing to solve and to physically understand this major issue. Most remarkably, our improved scheme demands to go beyond the paradigm of using the exact eigenvectors on graphs.
PACS: 05.30.-d – Quantum statistical mechanics / 71.27.+a – Strongly correlated electron systems; heavy fermions / 75.10.Jm – Quantized spin models, including quantum spin frustration
© EPLA, 2015