Dresden 2026 – scientific programme

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MA: Fachverband Magnetismus

MA 58: Computational Magnetism II

MA 58.8: Talk

Friday, March 13, 2026, 11:30–11:45, POT/0151

Dynamical mean-field theory for spin systems at finite temperature: cluster extension — •Przemyslaw Bieniek¹, Timo Grässer², and Götz Uhrig¹ — ¹Condensed Matter Theory, TU Dortmund University, Otto-Hahn-Str. 4, 44227 Dortmund, Germany — ²Institute of Molecular Physical Science, ETH Zürich, Vladimir-Prelog-Weg 1-5/10, 8093 Zürich, Switzerland

Dynamical mean-field theory (DMFT) is an established numerical technique for approximately solving fermionic many-body problems. It maps the full quantum system to an impurity problem and uses a self-consistency condition to connect back to expectation values of the original model. In recent years, a method inspired by DMFT applicable to spin systems (spinDMFT) was developed. It is in agreement with numerical techniques and has already proven successful in explaining nuclear magnetic resonance experiments. However, it was derived only in the case of infinite temperature.

Based on spinDMFT, we develop a dynamical mean-field theory for spin systems at finite temperatures. The algorithm computes spin correlations in imaginary time. It maps the spin system to a single-site problem with a time-dependent mean field and uses a self-consistency condition to connect the values of the mean-field to quantum expectation values. The single-site approach is extended to a cluster algorithm, allowing for the computation of nonlocal expectation values. We benchmark the algorithm by comparing the resulting correlations with numerical approaches. We discuss the potential applications of the method and possible extensions.

Keywords: Disordered spin systems; Mean-field theory; Computational techniques; Nuclear magnetic resonance