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

• Verfasst von: Mihaila, Luminita [VerfasserIn]
• Verfasst von: Zerf, Nikolai [VerfasserIn]
• Verfasst von: Scherer, Michael [VerfasserIn]
• Verfasst von: Ihrig, Bernhard [VerfasserIn]
• Titel: Gross-Neveu-Yukawa model at three loops and Ising critical behavior of Dirac systems
• Verf.angabe: Luminita N. Mihaila, Nikolai Zerf, Bernhard Ihrig, Igor F. Herbut, and Michael M. Scherer
• Fussnoten: Gesehen am 14.11.2017
• Titel Quelle: Enthalten in: Physical review
• Jahr Quelle: 2017
• Band/Heft Quelle: 96(2017,16) Artikel-Nummer 165133, 6 Seiten
• ISSN Quelle: 2469-9969
• DOI: doi:10.1103/PhysRevB.96.165133
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1565313941

Abstract

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.