Scaling at quantum phase transitions above the upper critical dimension

Langheld, Anja; Koziol, Jan Alexander; Adelhardt, Patrick; Kapfer, Sebastian; Schmidt, Kai Phillip

doi:10.21468/SciPostPhys.13.4.088

SciPost Physics

Scaling at quantum phase transitions above the upper critical dimension

A. Langheld, J. A. Koziol, P. Adelhardt, S. C. Kapfer, K. P. Schmidt

SciPost Phys. 13, 088 (2022) · published 10 October 2022

doi: 10.21468/SciPostPhys.13.4.088
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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.

This publication has been updated

Correction: Scaling at quantum phase transitions above the upper critical dimension on 2022-11-04

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.13.4.088
TI  - Scaling at quantum phase transitions above the upper critical dimension
PY  - 2022/10/10
UR  - https://scipost.org/SciPostPhys.13.4.088
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 13
IS  - 4
SP  - 088
A1  - Langheld, Anja
AU  - Koziol, Jan Alexander
AU  - Adelhardt, Patrick
AU  - Kapfer, Sebastian
AU  - Schmidt, Kai Phillip
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.13.4.088,
	title={{Scaling at quantum phase transitions above the upper critical dimension}},
	author={A. Langheld and J. A. Koziol and P. Adelhardt and S. C. Kapfer and K. P. Schmidt},
	journal={SciPost Phys.},
	volume={13},
	pages={088},
	year={2022},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.13.4.088},
	url={https://scipost.org/10.21468/SciPostPhys.13.4.088},
}

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¹ Friedrich-Alexander-Universität Erlangen-Nürnberg / University of Erlangen-Nuremberg [FAU]

Funder for the research work leading to this publication

Deutsche Forschungsgemeinschaft / German Research FoundationDeutsche Forschungsgemeinschaft [DFG]