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

TL;DR

This paper investigates the quantum critical behavior of antiferromagnetism in graphene and similar gapless systems using mean-field theory, revealing how critical exponents depend on the density of states exponent r.

Contribution

It develops a generalized mean-field theory for gapless phases with density of states |E|^r, showing how critical exponents vary with r and extending quantum criticality analysis to bulk correlated phases.

Findings

For r>2, conventional mean-field exponents are recovered.

For -1<r<2, critical exponents depend significantly on r.

Finite critical interaction exists for r>0, indicating no weak-coupling solution in this range.

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 \'a 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.