Lattice Field Theory Study of Magnetic Catalysis in Graphene

Abstract

We discuss the simulation of the low-energy effective field theory (EFT) for graphene in the presence of an external magnetic field. Our fully nonperturbative calculation uses methods of lattice gauge theory to study the theory using a hybrid Monte Carlo approach. We investigate the phenomenon of magnetic catalysis in the context of graphene by studying the chiral condensate which is the order parameter characterizing the spontaneous breaking of chiral symmetry. In the EFT, the symmetry breaking pattern is given by $U(4)\to U(2)\times U(2)$. We also comment on the difficulty, in this lattice formalism, of studying the time-reversal-odd condensate characterizing the ground state in the presence of a magnetic field. Finally, we study the mass spectrum of the theory, in particular the Nambu-Goldstone (NG) mode as well as the Dirac quasiparticle, which is predicted to obtain a dynamical mass.

17 pages, 11 figures

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Cited by in corpus (15)

• Fermion bag approach to Hamiltonian lattice field theories in continuous time
• Hybrid-Monte-Carlo study of competing order in the extended fermionic Hubbard model on the hexagonal lattice
• Surface Magnetic Catalysis
• Numerical evidence of conformal phase transition in graphene with long-range interactions
• Quantum Monte Carlo study of static potential in graphene
• Field theoretic renormalization study of reduced quantum electrodynamics and applications to the ultra-relativistic limit of Dirac liquids
• Collective charge excitations and the metal-insulator transition in the square lattice Hubbard-Coulomb model
• Absence of inhomogeneous chiral phases in 2+1-dimensional four-fermion and Yukawa models
• Field theoretic study of electron-electron interaction effects in Dirac liquids
• Direct detection of metal-insulator phase transitions using the modified Backus-Gilbert method
• Lattice Quantum Monte Carlo Study of Chiral Magnetic Effect in Dirac Semimetals
• Quantum criticality of magnetic catalysis in two-dimensional correlated Dirac fermions
• Lattice field theory simulations of Dirac semimetals
• Incompressible Even Denominator Fractional Quantum Hall States in the Zeroth Landau Level of Monolayer Graphene
• Dirac Kondo effect under magnetic catalysis