Scaling at quantum phase transitions above the upper critical dimension

Langheld A, Koziol J, Adelhardt P, Kapfer S, Schmidt KP (2022)

Publication Type: Journal article

Publication year: 2022

Journal

Book Volume: 13

Article Number: 088

Journal Issue: 4

DOI: 10.21468/SciPostPhys.13.4.088

Abstract

The hyperscaling relation and standard finite-size scaling (FSS) are known to break down above the upper critical dimension due to dangerous irrelevant variables. We establish a coherent formalism for FSS at quantum phase transitions above the upper critical dimension following the recently introduced Q-FSS formalism for thermal phase transitions. Contrary to long-standing belief, the correlation sector is affected by dangerous irrelevant variables. The presented formalism recovers a generalized hyperscaling relation and FSS form. Using this new FSS formalism, we determine the full set of critical exponents for the long-range transverse-field Ising chain in all criticality regimes ranging from the nearest-neighbor to the long-range mean-field regime. For the same model, we also explicitly confirm the effect of dangerous irrelevant variables on the characteristic length scale.

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APA:

Langheld, A., Koziol, J., Adelhardt, P., Kapfer, S., & Schmidt, K.P. (2022). Scaling at quantum phase transitions above the upper critical dimension. SciPost Physics, 13(4). https://doi.org/10.21468/SciPostPhys.13.4.088

MLA:

Langheld, Anja, et al. "Scaling at quantum phase transitions above the upper critical dimension." SciPost Physics 13.4 (2022).

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