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TT: Fachverband Tiefe Temperaturen

TT 37: Correlated Electrons: Poster

TT 37.51: Poster

Mittwoch, 19. März 2025, 15:00–18:00, P4

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

We derive effective block-diagonal Hamiltonians H_eff = T^†H T using the projective-cluster additive transformation (PCAT) [1]. Numerical linked-cluster expansions (NLCEs) are employed to study the (anti)ferromagnetic transverse-field Ising model (TFIM) on diverse lattice geometries such as chains and various ladders. By calculating energy gaps, we compare the scaling behavior with other methods such as deepCUT [2]. A key challenge arises from the presence of avoided-level crossings (ALCs) [3] which complicates convergence. To probe this issue, we analyze ALCs in the simplified setting of the XXZ model on a chain. A key property of PCAT is the cluster additivity of both H_eff and the generator S = log(T). This allows transforming larger systems via a cluster expansion in S. Using S from clusters up to size N, we compute exp(−S) H exp(S) in the thermodynamic limit and compare it with standard NLCE and CUT methods [4]. Notably, S for local clusters generates higher-order terms, mitigating some scaling challenges in traditional cluster expansions.

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

[2] H. Krull et al., Phys. Rev. B 86.

[3] K. Coester et al., EPL, 110(2):20006.

[4] C. Knetter et al., EPJ B 13:209.

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