A. Langheld, J. A. Koziol, P. Adelhardt, S. C. Kapfer, K. P. Schmidt
SciPost Phys. 13, 088 (2022) ·
published 10 October 2022
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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.
