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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| Main Authors: | , , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
17 October 2017
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| 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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| 520 | |a 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. | ||
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