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Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems

Dirac and Weyl fermions appear as quasiparticle excitations in many different condensed-matter systems. They display various quantum transitions which represent unconventional universality classes related to the variants of the Gross-Neveu model. In this paper we study the bosonized version of the s...

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Bibliographic Details
Main Authors: Mihaila, Luminita (Author) , Zerf, Nikolai (Author) , Scherer, Michael (Author) , Ihrig, Bernhard (Author)
Format: Article (Journal)
Language:English
Published: 17 October 2017
In: Physical review
Year: 2017, Volume: 96, Issue: 16, Pages: 165133
ISSN:2469-9969
DOI:10.1103/PhysRevB.96.165133
Online Access:Verlag, Volltext: http://dx.doi.org/10.1103/PhysRevB.96.165133
Verlag, Volltext: https://link.aps.org/doi/10.1103/PhysRevB.96.165133
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Author Notes:Luminita N. Mihaila, Nikolai Zerf, Bernhard Ihrig, Igor F. Herbut, and Michael M. Scherer
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Summary:Dirac and Weyl fermions appear as quasiparticle excitations in many different condensed-matter systems. They display various quantum transitions which represent unconventional universality classes related to the variants of the Gross-Neveu model. In this paper we study the bosonized version of the standard Gross-Neveu model—the Gross-Neveu-Yukawa theory—at three-loop order, and compute critical exponents in 4−ε dimensions for a general number of fermion flavors. Our results fully encompass the previously known two-loop calculations, and agree with the known three-loop results in the purely bosonic limit of the theory. We also find the exponents to satisfy the emergent superscaling relations in the limit of a single-component fermion, order by order up to three loops. Finally, we apply the computed series for the exponents and their Padé approximants to several phase transitions of current interest: metal-insulator transitions of spin-1/2 and spinless fermions on the honeycomb lattice, emergent supersymmetric surface field theory in topological phases, as well as the disorder-induced quantum transition in Weyl semimetals. Comparison with the results of other analytical and numerical methods is discussed.
Item Description:Gesehen am 14.11.2017
Physical Description:Online Resource
ISSN:2469-9969
DOI:10.1103/PhysRevB.96.165133

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