Universität zu Köln

Ihrig, Bernhard, Mihaila, Luminita N. and Scherer, Michael M. ORCID: 0000-0003-0766-9949 (2018). Critical behavior of Dirac fermions from perturbative renormalization. Phys. Rev. B, 98 (12). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2469-9969

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Abstract

Gapless Dirac fermions appear as quasiparticle excitations in various condensed-matter systems. They feature quantum critical points with critical behavior in the 2+1-dimensional Gross-Neveu universality class. The precise determination of their critical exponents defines a prime benchmark for complementary theoretical approaches, such as lattice simulations, the renormalization group, and the conformal bootstrap. Despite promising recent developments in each of these methods, however, no satisfactory consensus on the fermionic critical exponents has been achieved, so far. Here, we perform a comprehensive analysis of the Ising Gross-Neveu universality classes based on the recently achieved four-loop perturbative calculations. We combine the perturbative series in 4 - epsilon spacetime dimensions with the one for the purely fermionic Gross-Neveu model in 2 + epsilon dimensions by employing polynomial interpolation as well as two-sided Pade approximants. Further, we provide predictions for the critical exponents exploring various resummation techniques following the strategies developed for the three-dimensional scalar O(n) universality classes. We give an exhaustive appraisal of the current situation of Gross-Neveu universality by comparison to other methods. For a large enough number of spinor components N >= 8 as well as for the case of emergent supersymmetry N = 1, we find our renormalization group estimates to be in excellent agreement with the conformal bootstrap, building a strong case for the validity of these values. For intermediate N as well as in comparison with recent Monte Carlo results, deviations are found and critically discussed.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Ihrig, Bernhard UNSPECIFIED UNSPECIFIED UNSPECIFIED Mihaila, Luminita N. UNSPECIFIED UNSPECIFIED UNSPECIFIED Scherer, Michael M. UNSPECIFIED orcid.org/0000-0003-0766-9949 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-173228
DOI:	10.1103/PhysRevB.98.125109
Journal or Publication Title:	Phys. Rev. B
Volume:	98
Number:	12
Date:	2018
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2469-9969
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language GROSS-NEVEU MODEL; CONFORMAL BOOTSTRAP CALCULATION; CRITICAL EXPONENT-ETA; BOREL SUMMABILITY; 1/N EXPANSION; COMPUTATION; GRAPHENE; ORDER; DIMENSION; O(1/N2) Multiple languages Materials Science, Multidisciplinary; Physics, Applied; Physics, Condensed Matter Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/17322