Scaling at quantum phase transitions above the upper critical dimension

• URL: http://arxiv.org/abs/2203.08081v2
• Date: Fri, 8 Jul 2022 19:28:43 GMT
• Title: Scaling at quantum phase transitions above the upper critical dimension
• Authors: A. Langheld, J.A. Koziol, P. Adelhardt, S.C. Kapfer, K.P. Schmidt
• Abstract summary: We establish a coherent formalism for FSS at quantum phase transitions above the upper critical dimension. Contrary to long-standing belief, the correlation sector is affected by dangerous irrelevant variables.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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