Pavel Buividovich

Numerical study of chiral symmetry breaking in non-Abelian gauge theory with background magnetic field

Abstract We investigate the effect of a uniform background magnetic field on the chiral symmetry breaking in SU ( 2 ) Yang–Mills theory on the lattice. We observe that the chiral condensate grows linearly with the field strength B up to e B = 3 GeV as predicted by chiral perturbation theory for full QCD. As the temperature increases the coefficient in front of the linear term gets smaller. In the magnetic field near-zero eigenmodes of the Dirac operator tend to have more regular structure with larger (compared to zero-field case) Hausdorff dimensionality. We suggest that the delocalization of near-zero eigenmodes plays a crucial role in the enhancement of the chiral symmetry breaking.

Quark electric dipole moment induced by magnetic field

We show numerically that quarks develop an electric dipole moment in the direction of a sufficiently intense magnetic field due to local fluctuations of topological charge. This anomalous CP-odd effect is a spin analogue of the chiral magnetic effect in QCD.

Fractal dimension of the topological charge density distribution in SU(2) lattice gluodynamics

DESY, Notkestrasse 85, 22607 Hamburg, Germany(Dated: December 3, 2011)We study the effect of cooling on the spatial distribution of the topological charge density inquenched SU(2) lattice gauge theory with overlap fermions. We show that as the gauge field con-figurations are cooled, the Hausdorff dimension of regions where the topological charge is localizedgradually changes from d = 2 ÷3 towards the total space dimension. Hence the cooling proceduredestroys some of the essential properties of the topological charge distribution.

Numerical study of chiral magnetic effect in quenched SU(2) lattice gauge theory

A possible experimental observation of the chiral magnetic effect in heavy ion collisions at RHIC was recently reported by the STAR Collaboration. We study signatures of this effect in SU(2) lattice gluodynamics with the chirally invariant Dirac operator. We find that at zero temperature the local fluctuations of an electric current of quarks and chirality fluctuations increase with external Abelian magnetic field. The external magnetic field leads to spatial separation of the quarks electric charges. The separation increases with the strength of the magnetic field. As temperature gets higher the dependence of these quantities on the strength of the magnetic field becomes weaker. In the deconfinement phase the local fluctuations of the chiral density and of the spatial components of the quarks electric current are large and are almost independent on the external magnetic field. The local fluctuations of the electric charge density decrease with the strength of the magnetic field in this phase.

Topological and magnetic properties of the QCD vacuum probed by overlap fermions

We study some of the local CP-odd and magnetic properties of the non-Abelian vacuum with use of overlap fermions within the quenched lattice gauge theory. Among these properties are the following: inhomogeneous spatial distribution of the topological charge density (chirality for massless fermions) in SU(2) gluodynamics (for uncooled gauge configurations the chirality is localized on low-dimensional defects with d=2..3, while a sequence of cooling steps gives rise to four-dimensional instantons and hence a four-dimensional structure of the chirality distribution); finite local fluctuations of the chirality growing with the strength of an external magnetic field; magnetization and susceptibility of the QCD vacuum in SU(3) theory; magnetic catalysis of the chiral symmetry breaking, and the electric conductivity of the QCD vacuum in strong magnetic fields.

Numerical Study of Nonperturbative Corrections to the Chiral Separation Effect in Quenched Finite-Density QCD

We demonstrate the nonrenormalization of the chiral separation effect (CSE) in quenched finite-density QCD in both confinement and deconfinement phases using a recently developed numerical method which allows us, for the first time, to address the transport properties of exactly chiral, dense lattice fermions. This finding suggests that CSE can be used to fix renormalization constants for axial current density. Explaining the suppression of the CSE which we observe for topologically nontrivial gauge field configurations on small lattices, we also argue that CSE vanishes for self-dual non-Abelian fields inside instanton cores.

Competing order in the fermionic Hubbard model on the hexagonal graphene lattice

We study the phase diagram of the fermionic Hubbard model on the hexagonal lattice in the space of on-site and nearest neighbor couplings with Hybrid-Monte-Carlo simulations. With pure on-site repulsion this allows to determine the critical coupling strength for spin-density wave formation with the standard approach of introducing a small mass term, explicitly breaking the sublattice symmetry. The analogous mass term for charge-density wave formation above a critical nearest-neighbor repulsion, on the other hand, would introduce a fermion sign problem. The competition between the two and the phase diagram in the space of the two coouplings can however be studied in simulations without explicit sublattice symmetry breaking. Our results compare qualitatively well with the Hartree-Fock phase diagram. We furthermore demonstrate how spin-symmetry breaking by the Euclidean time discretization can be avoided also, when using an improved fermion action based on an exponetial transfer matrix with exact sublattice symmetry.

First experience with classical-statistical real-time simulations of anomalous transport with overlap fermions

We present first results of classical-statistical real-time simulations of anomalous transport phenomena with overlap fermions. We find that even on small lattices overlap fermions reproduce the real-time anomaly equation with much better precision than Wilson-Dirac fermions on an order of magnitude larger lattices. The difference becomes much more pronounced for quickly changing electromagnetic fields, especially if one takes into account the back-reaction of fermions on electromagnetism. As test cases, we consider chirality pumping in parallel electric and magnetic fields and mixing between the plasmon and the Chiral Magnetic Wave.

Chiral Magnetic Effect in finite-size samples of parity-breaking Weyl semimetals

We study the static electric current due to the Chiral Magnetic Effect in samples of Weyl semimetals with slab geometry, where the magnetic field is parallel to the boundaries of the slab. We use the Wilson-Dirac Hamiltonian as a simplest model of parity-breaking Weyl semimetal with two-band structure. We find that the CME current is strongly localized at the open boundaries of the slab, where the current density in the direction of the magnetic field approaches the conventional value

A numerical method to compute derivatives of functions of large complex matrices and its application to the overlap Dirac operator at finite chemical potential

j = \mu_5 B /2 \pi^2