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We present results of a study of the Chiral Separation Effect (CSE) in quenched finite-density QCD. Using a recently developed numerical method we calculate the conserved axial current for exactly chiral overlap fermions at finite density for the first time. We compute the anomalous transport coefficient for the CSE in the confining and de-confining phase and investigate possible deviations from the universal value. In both phases we find that non-perturbative corrections to the CSE are absent and we reproduce the universal value for the transport coefficient within small statistical errors. Our results suggest that the CSE can be used to determine the renormalisation factor of the axial current., Comment: 8 pages, 3 figures, to appear in the proceedings of the Lattice 2017 conference (18-24 June 2017, Granada, Spain)

We demonstrate the non-renormalization 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, 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., Comment: 6 + 2 pages, 3 figures, 1 table, REVTeX style, conclusion changed due to results from simulations with larger lattices, accepted for publication in PRL

A recently developed numerical method for the calculation of derivatives of functions of general complex matrices, which can also be combined with implicit matrix function approximations such as Krylov-Ritz type algorithms, is presented. An important use case for the method in the context of lattice gauge theory is the overlap Dirac operator at finite quark chemical potential. Derivatives of the lattice Dirac operator are necessary for the computation of conserved lattice currents or the fermionic force in Hybrid Monte-Carlo and Langevin simulations. To calculate the overlap Dirac operator at finite chemical potential the product of the sign function of a non-Hermitian matrix with a vector has to be computed. For non-Hermitian matrices it is not possible to efficiently approximate the sign function with polynomials or rational functions. Implicit approximation algorithms, like Krylov-Ritz methods, that depend on the source vector have to be used instead. Our method can also provide derivatives of such implicit approximations. We show how a generalised deflation prescription can be used to improve the performance of the method, if some eigenvalues and eigenvectors of the matrix being differentiated are known. To show that the method is efficient and well suited for practical calculations we provide test results for the two-sided Lanczos approximation of the finite-density overlap Dirac operator on SU(3) gauge field configurations on lattices with sizes up to $14 \times 14^3$., Comment: 7 pages PoS style, 2 figures, to appear in the proceedings of the Lattice 2016 conference (24-30 July 2016, University of Southampton, UK)

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 $SU(3)$ gauge field configurations on lattices with sizes as large as $14\times14^3$ and $6\times18^3$., Comment: 26 pages elsarticle style, 5 figures minor text changes, journal version

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 $j = \mu_5 B /2 \pi^2$ at sufficiently small values of the chiral chemical potential $\mu_5$ and magnetic field $B$. On the other hand, very large values of magnetic field tend to suppress the CME response. We observe that the localization width of the current is independent of the slab width and is given by the magnetic length $l_B = 1/\sqrt{B}$ when $\mu_5 \ll \sqrt{B}$. In the opposite regime when $\mu_5 \gg \sqrt{B}$ the localization width is determined solely by $\mu_5$, Comment: 9 pages PoS style, 5 figures, to appear in the proceedings of the Lattice 2015 conference (14-18 July 2015, Kobe, Japan)

We report on the mean-field study of the Chiral Magnetic Effect (CME) in static magnetic fields within a simple model of a parity-breaking Weyl semimetal given by the lattice Wilson-Dirac Hamiltonian with constant chiral chemical potential. We consider both the mean-field renormalization of the model parameters and nontrivial corrections to the CME originating from re-summed ladder diagrams with arbitrary number of loops. We find that on-site repulsive interactions affect the chiral magnetic conductivity almost exclusively through the enhancement of the renormalized chiral chemical potential. Our results suggest that nontrivial corrections to the chiral magnetic conductivity due to inter-fermion interactions are not relevant in practice, since they only become important when the CME response is strongly suppressed by the large gap in the energy spectrum., Comment: 19 pages RevTeX, 13 figures

The overlap Dirac operator obeys the Ginsparg-Wilson equation and offers a possibility to introduce chiral symmetry on the lattice. Evaluating the overlap operator is numerically very expensive and one has to rely on approximation methods. At finite chemical potential the overlap operator can be efficiently computed with the two-sided Lanczos algorithm. To calculate conserved currents on the lattice, or to evaluate the fermionic force in HMC calculations, one needs to compute derivatives of the Dirac operator with respect to gauge fields. In this paper we present a method to simultaneously compute the action of the overlap operator and its derivative on a source vector., Comment: 7 pages PoS style, 1 figure, to appear in the proceedings of the Lattice 2014 conference (23-28 June 2014, Columbia University, New York, USA)

We perform a mean-field study of the phase diagram of interacting Weyl semimetals with broken parity, that is, with different densities of right- and left-handed quasiparticles. As a simple model system, we consider the Wilson-Dirac Hamiltonian with the chiral chemical potential and on-site repulsive interactions. We find that the chiral chemical potential somewhat shrinks the region of the pion condensation (Aoki phase) in the parameter space of the bare mass and the interaction strength, so that the condensation thresholds are at smaller interaction strengths. The renormalized chiral chemical potential monotonously grows with interaction strength everywhere in the phase diagram, and only the growth rate is discontinuous across the phase transition lines. These findings are in full agreement with previous results obtained by one of the authors for the continuum Dirac Hamiltonian, except for the fact that for our lattice model with explicitly broken chiral symmetry the boundaries of the Aoki phase remain sharp second-order phase transitions even at nonzero chiral chemical potential and there are no signatures of Cooper-type instabilities in the weakly interacting regime., Comment: 7 pages PoS style, 2 figures, to appear in the proceedings of the Lattice 2014 conference (23-28 June 2014, Columbia University, New York, USA)