Erlangen 2022 – scientific programme

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SYQC: Symposium Quantum Cooperativity of Light and Matter

SYQC 3: Quantum Cooperativity (joint session Q/SYQC)

SYQC 3.6: Talk

Friday, March 18, 2022, 11:45–12:00, Q-H15

Finite-Size Scaling at Quantum Phase Transitions Above the Upper Critical Dimension — •Anja Langheld, Jan Alexander Koziol, Patrick Adelhardt, Sebastian C. Kapfer, and Kai Phillip Schmidt — Lehrstuhl für Theoretische Physik I, Staudtstraße 7, Friedrich-Alexander Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany

We present a modern formalism for finite-size scaling (FSS) at quantum phase transitions (QPT) above the upper critical dimension. The upper critical dimension becomes experimentally accessible, for instance, in systems with long-range interactions such as the long-range transverse-field Ising model, which can be realized in systems of trapped ions. In general, FSS at phase transitions above the upper critical dimension requires a special treatment as dangerous irrelevant variables (DIV) lead to modifications in the homogeneity laws, thereby causing the breakdown of hyperscaling and standard FSS. Following the recently developed Q-FSS formalism addressing this issue for thermal phase transitions, we transfer the idea to QPT while stressing the subtle differences and connections to the classical version. By relaxing the long-standing belief that the correlation length is unaffected by DIV, the presented FSS formalism fixes the aforementioned issues above the upper critical dimension and recovers a generalized hyperscaling relation. The influence of DIV on the correlation length is explicitly confirmed using numerical calculations of the long-range transverse-field Ising model.