Numerical study of chiral plasma instability within the classical statistical field theory approach

We report on a numerical study of real-time dynamics of electromagnetically interacting chirally imbalanced lattice Dirac fermions within the classical statistical field theory approach. Namely, we perform exact simulations of the real-time quantum evolution of fermionic fields coupled to classical electromagnetic fields, which are in turn coupled to the vacuum expectation value of the fermionic electric current. We use Wilson-Dirac Hamiltonian for fermions, and non-compact action for the gauge field. In general, we observe that the backreaction of fermions on the electromagnetic field prevents the system from acquiring chirality imbalance. In the case of chirality pumping in parallel electric and magnetic fields, electric field is screened by the produced on-shell fermions and the accumulation of chirality is hence stopped. In the case of evolution with initially present chirality imbalance, axial charge tends to transform to helicity of electromagnetic field. By performing simulations on large lattices we show that in most cases this decay process is accompanied by the inverse cascade phenomenon which transfers energy from short-wavelength to long-wavelength electromagnetic fields. In some simulations, however, we observe a very clear signature of inverse cascade for the helical magnetic fields which is not accompanied by the axial charge decay. This suggests that the relation between inverse cascade and axial charge decay is not as straightforward as predicted by the simplest form of anomalous Maxwell equations.Comment: 22 pages RevTeX, 14 figures; v4: published version, updated references, new physical results on large lattice

Applications of lattice QCD techniques for condensed matter systems

We review the application of lattice QCD techniques, most notably the Hybrid Monte-Carlo (HMC) simulations, to first-principle study of tight-binding models of crystalline solids with strong inter-electron interactions. After providing a basic introduction into the HMC algorithm as applied to condensed matter systems, we review HMC simulations of graphene, which in the recent years have helped to understand the semi-metal behavior of clean suspended graphene at the quantitative level. We also briefly summarize other novel physical results obtained in these simulations. Then we comment on the applicability of Hybrid Monte-Carlo to topological insulators and Dirac and Weyl semi-metals and highlight some of the relevant open physical problems. Finally, we also touch upon the lattice strong-coupling expansion technique as applied to condensed matter systems.Comment: 20 pages, 5 figures, Contribution to IJMPA special issue "Lattice gauge theory beyond QCD". List of references update

Magnetism and interaction-induced gap opening in graphene with vacancies or hydrogen adatoms: Quantum Monte Carlo study

We study electronic properties of graphene with finite concentration of vacancies or other resonant scatterers by a straightforward lattice Quantum Monte Carlo calculations. Taking into account realistic long-range Coulomb interaction we calculate distribution of spin density associated to midgap states and demonstrate antiferromagnetic ordering. Energy gaps are open due to the interaction effects, both in the bare graphene spectrum and in the vacancy/impurity bands. In the case of 5 % concentration of resonant scatterers the latter gap is estimated as 0.7 eV and 1.1 eV for graphene on boron nitride and freely suspended graphene, respectively.Comment: Text is substantially updated, temperature dependence of order parameter is added. Accepted for publication in PR

Green functions in graphene monolayer with Coulomb interactions taken into account

We consider the low energy effective field model of graphene monolayer. Coulomb interactions are taken into account. The model is simulated numerically using the lattice discretization with staggered fermions. The two point fermionic Green functions are calculated. We find that in the insulator phase these Green functions almost do not depend on energy. This indicates that the effective field model (in its insulator phase) does not correspond to the real graphene.Comment: Latex, 9 pages, accepted for publication in Solid State Communication