Abstract

We renormalize the Gross-Neveu-Yukawa model with an O(N) symmetry to O(ϵ5) in d = 4 −ϵ dimensions and determine the anomalous dimensions of the fermion and scalar fields, β-functions as well as the scalar field’s mass operator. These are used to construct several N dependent critical exponents relevant for quantum transitions in semi-metals and in particular those connected with graphene in three dimensions when N = 2. Improved exponent estimates for scalar fermion transitions on a honeycomb lattice, when N = 1, as well as for N = 5 are also given to compare with results from other techniques such as the conformal bootstrap.

Abstract

We renormalize the Gross-Neveu-Yukawa model with an O(N) symmetry to O(ϵ5) in d = 4 −ϵ dimensions and determine the anomalous dimensions of the fermion and scalar fields, β-functions as well as the scalar field’s mass operator. These are used to construct several N dependent critical exponents relevant for quantum transitions in semi-metals and in particular those connected with graphene in three dimensions when N = 2. Improved exponent estimates for scalar fermion transitions on a honeycomb lattice, when N = 1, as well as for N = 5 are also given to compare with results from other techniques such as the conformal bootstrap.

Abstract

We renormalize the Gross-Neveu-Yukawa model with an O(N) symmetry to O(ϵ5) in d = 4 −ϵ dimensions and determine the anomalous dimensions of the fermion and scalar fields, β-functions as well as the scalar field’s mass operator. These are used to construct several N dependent critical exponents relevant for quantum transitions in semi-metals and in particular those connected with graphene in three dimensions when N = 2. Improved exponent estimates for scalar fermion transitions on a honeycomb lattice, when N = 1, as well as for N = 5 are also given to compare with results from other techniques such as the conformal bootstrap.

Abstract

We renormalize the Gross-Neveu-Yukawa model with an O(N) symmetry to O(ϵ5) in d = 4 −ϵ dimensions and determine the anomalous dimensions of the fermion and scalar fields, β-functions as well as the scalar field’s mass operator. These are used to construct several N dependent critical exponents relevant for quantum transitions in semi-metals and in particular those connected with graphene in three dimensions when N = 2. Improved exponent estimates for scalar fermion transitions on a honeycomb lattice, when N = 1, as well as for N = 5 are also given to compare with results from other techniques such as the conformal bootstrap.