150 research outputs found
Anomalous transport with overlap fermions
Anomalous correlators of vector and axial currents which enter the Kubo
formulae for the chiral magnetic and the chiral separation conductivities are
explicitly calculated for free overlap fermions on the lattice. The results are
confronted with continuum calculations in the finite-temperature
regularization, and a subtle point of such regularization for chiral magnetic
conductivity related to the correct counting of the chiral states is
highlighted. In agreement with some previous claims in the literature, we find
that in a lattice regularization which respects gauge invariance, the chiral
magnetic conductivity vanishes. We point out that the relation of anomalous
transport coefficients to axial anomaly is nontrivial due to the
non-commutativity of their infrared limit and the Taylor expansion in baryon or
chiral chemical potential. In particular, we argue that the vector and axial
Ward identities fix the asymptotic behavior of anomalous current-current
correlators in the limit of large momenta. Basing on the work of Knecht et al.
on the perturbative non-renormalization of the transverse part of the
correlator of two vector and one axial currents, we demonstrate that the
relation of the anomalous vector-vector correlator to axial anomaly holds
perturbatively in massless QCD but might be subject to non-perturbative
corrections. Finally, we identify kinematical regimes in which the anomalous
transport coefficients can be extracted from lattice measurements.Comment: 25 pages RevTex, 7 figures; v2: published version, discussion of CME
improve
Overlap Dirac operator with chiral chemical potential and Chiral Magnetic Effect on the lattice
A self-consistent construction of the overlap lattice Dirac operator coupled
to chiral chemical potential is proposed. With the help of the constructed
operator we compute electric current induced by a constant magnetic field
(Chiral Magnetic Effect). We find that the result disagrees with the one
predicted by anomaly-based arguments and comment on the origin of this
discrepancy. We demonstrate that a straightforward lattice calculation with a
constant magnetic field and a uniform chiral chemical potential in fact
corresponds to an infrared singularity in the dimensionally reduced
polarization tensor and hence yields the result which is extremely sensitive to
infrared regulators such as finite volume or finite temperature.Comment: 7 pages, 2 figures; to appear in the proceedings of the Lattice2013
conference (July 29th - August 3rd 2013, Mainz, Germany
Surface states of massive Dirac fermions with separated Weyl nodes
We derive the spectra of surface states for massive Dirac Hamiltonians with
either momentum or energy separation between the left- and right-handed Weyl
nodes. Momentum separation between the Weyl nodes corresponds to the explicitly
broken time-reversal symmetry and the energy separation - to broken parity.
Such Hamiltonians provide the simplest model description of Weyl semimetals. We
find that the only effect of the energy separation between the Weyl nodes is to
decrease the Fermi velocity in the linear dispersion relation of the surface
states of massive Dirac Hamiltonian. In the case of broken time-reversal
symmetry, the spectrum of surface states interpolates in a nontrivial way
between the Fermi arc-type and the Dirac cone-type dispersion relations. In
particular we find that for all values of the mass and the momentum separation
between the Weyl nodes the surface states only exist in a strip of finite width
in momentum space. We give also some simpler examples of surface states in
order to make these notes more pedagogical.Comment: 10 pages AIP proceedings style, 1 figure; Submitted to the
proceedings of the Confinement XI conference, Sept. 8-12, St. Petersburg,
Russia; partly includes the material of the lectures given by the author at
the 2014 Parma International School of Theoretical Physics; v2: updated
reference
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
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