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I discuss the competition of spin- and charge-density waves and their quantum multicritical behavior for the semimetal-insulator transitions of low-dimensional Dirac fermions. Employing the effective Gross-Neveu-Yukawa theory with two order parameters as a model for graphene and a growing number of other two-dimensional Dirac materials allows us to describe the physics near the multicritical point at which the semimetallic and the two ordered phases meet. With the functional renormalization group approach, we reveal a complex structure of fixed points. Their the stability properties decisively depend on the number of Dirac fermions Nf. We give estimates for the critical exponents and observe crucial quantitative corrections as compared to a previous first-order epsilon expansion. For small Nf, the universal behavior near the multicritical point is determined by the chiral Heisenberg universality class supplemented by a decoupled, purely bosonic, Ising sector. At large Nf, a novel fixed point with nontrivial couplings between all sectors becomes stable. At intermediate Nf, including the graphene case (Nf=2) no stable and physically admissible fixed point exists. We therefore suggest that Graphene's phase diagram in the vicinity of the intersection between the semimetal, antiferromagnetic and staggered density phases is governed by a triple point exhibiting first-order transitions.

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Michael Scherer, University of Heidelberg
Seminar Room 0.03, ETP
Contact: Philipp Strack