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 (22)

• 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
• Non-Fermi liquid behaviour of electrons in the half-filled honeycomb lattice (A renormalization group approach)
• Is graphene in vacuum an insulator?
• Theory of interacting electrons on the honeycomb lattice
• Chiral Decomposition in the Electronic Structure of Graphene Multilayers
• Tight-binding modeling and low-energy behavior of the semi-Dirac point
• Lattice field theory simulations of graphene
• Relativistic Mott criticality in graphene
• Ground state and finite temperature signatures of quantum phase transitions in the half-filled Hubbard model on a honeycomb lattice
• Phase diagram and magnetic collective excitations of the Hubbard model in graphene sheets and layers
• Gap generation and semimetal-insulator phase transition in graphene
• Magnetism of Finite Graphene Samples: Mean-Field Theory compared with Exact Diagonalization and Quantum Monte Carlo Simulation
• Reentrant violation of special relativity in the low-energy corner
• Critical exponents of the semimetal-insulator transition in graphene: A Monte Carlo study
• Nodal liquid and s-wave superconductivity in transition metal dichalcogenides
• The 2D Hubbard model on the honeycomb lattice
• Near Critical States of Random Dirac Fermions
• A fractional-spin phase in the power-law Kondo model
• Coulomb interaction and semimetal-insulator transition in graphene

Cited by in corpus (5)

• Flat bands in topological media
• Low frequency optical conductivity in graphene and in other scale-invariant two-band systems
• Phenomenology of a semi-Dirac semi-Weyl semi-metal
• Extended Hubbard model in undoped and doped monolayer and bilayer graphene: Selection rules and organizing principle among competing orders
• Phase Diagram Structure of Topological Mott Transition for Zero-gap Semiconductors beyond Conventional Landau-Ginzburg-Wilson Scenario