176 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
A numerical method to compute derivatives of functions of large complex matrices and its application to the overlap Dirac operator at finite chemical potential
We present a method for the numerical calculation of derivatives of functions
of general complex matrices. The method can be used in combination with any
algorithm that evaluates or approximates the desired matrix function, in
particular with implicit Krylov-Ritz-type approximations. An important use case
for the method is the evaluation of the overlap Dirac operator in lattice
Quantum Chromodynamics (QCD) at finite chemical potential, which requires the
application of the sign function of a non-Hermitian matrix to some source
vector. While the sign function of non-Hermitian matrices in practice cannot be
efficiently approximated with source-independent polynomials or rational
functions, sufficiently good approximating polynomials can still be constructed
for each particular source vector. Our method allows for an efficient
calculation of the derivatives of such implicit approximations with respect to
the gauge field or other external parameters, which is necessary for the
calculation of conserved lattice currents or the fermionic force in Hybrid
Monte-Carlo or Langevin simulations. We also give an explicit deflation
prescription for the case when one knows several eigenvalues and eigenvectors
of the matrix being the argument of the differentiated function. We test the
method for the two-sided Lanczos approximation of the finite-density overlap
Dirac operator on realistic gauge field configurations on lattices with
sizes as large as and .Comment: 26 pages elsarticle style, 5 figures minor text changes, journal
versio
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