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TT: Fachverband Tiefe Temperaturen

TT 80: Correlated Electrons: Poster

TT 80.50: Poster

Donnerstag, 21. März 2024, 15:00–18:00, Poster E

Convergence behaviour of numerical linked-cluster expansions — •Harald Leiser, Max Hörmann, and Kai Phillip Schmidt — Department Physik, Staudtstraße 7, Friedrich-Alexander Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany

An important step in understanding dynamical properties of quantum many-body systems is the investigation of one-particle properties in the thermodynamic limit. For a Hamiltonian H = H₀ + x V we derive an effective block-diagonal Hamiltonian H_eff = T^†H T^† with the projective cluster-additive transformation [1]. We calculated numerical linked-cluster expansions (NLCEs) for the antiferromagnetic transverse-field Ising model on a chain, ladder, triangular stripe and a sawtooth chain and obtained S = log (T) and H_eff. Moreover, we compared the convergence of the NLCE for the models under study with regards to the used unit cell expansion. Especially for the saw-tooth chain, a comparison with an expansion into triangles showed better agreements with extrapolations of existing series expansion [2]. Apart from that, we expand the framework to obtain one-particle properties more efficiently. To be concrete, we use the information on S of a cluster expansion up to a cluster-size with N spins to calculate exp(−S) H exp(S) in the thermodynamic limit and compare this with the usual NLCE up to the same cluster-size.

[1] M. Hörmann et al., SciPost Phys. 15 (2023) 097

[2] D. J. Priour et al., Phys. Rev. B 64 (2001) 134424

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