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arXiv · 2203.08081

Scaling at quantum phase transitions above the upper critical dimension

A. Langheld·J. A. Koziol·P. Adelhardt·S. C. Kapfer·K. P. Schmidt
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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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A. Langheld, J. A. Koziol, P. Adelhardt, S. C. Kapfer, K. P. Schmidt. 2022-03-15. Scaling at quantum phase transitions above the upper critical dimension. https://doi.org/10.21468/scipostphys.13.4.088

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