Mean-field quantum phase transition in graphene and in general gapless systems

Abstract

We study the quantum critical properties of antiferromagnetism in graphene at T=0 within mean-field (MF) theory. The resulting exponents differ from the conventional MF exponents, describing finite temperature transitions. Motivated by this, we have developed the MF theory of general gapless phases with density of states rho(E) |E|^r, r>-1, with the interaction as control parameter. For r>2, the conventional MF exponents á la Landau are recovered, while for -1<r<2, the exponents vary significantly with r. The critical interaction is finite for r>0, therefore no weak-coupling solution exists in this range. This generalizes the results on quantum criticality of the gapless Kondo systems to bulk correlated phases.

5 pages, 1 figure, 2 tables

References in corpus (8)

• The electronic properties of graphene
• The numerical renormalization group method for quantum impurity systems
• Emergence of magnetism in graphene materials and nanostructures
• Electronic states and Landau levels in graphene stacks
• Is graphene in vacuum an insulator?
• Theory of interacting electrons on the honeycomb lattice
• Chiral Decomposition in the Electronic Structure of Graphene Multilayers
• Lattice field theory simulations of graphene