Short-recurrence Krylov subspace methods for the overlap Dirac operator at nonzero chemical potential. (English) Zbl 1219.81096
Summary: The overlap operator in lattice QCD requires the computation of the sign function of a matrix, which is non-Hermitian in the presence of a quark chemical potential. In previous work we introduced an Arnoldi-based Krylov subspace approximation, which uses long recurrences. Even after the deflation of critical eigenvalues, the low efficiency of the method restricts its application to small lattices. Here we propose new short-recurrence methods which strongly enhance the efficiency of the computational method. Using rational approximations to the sign function we introduce two variants, based on the restarted Arnoldi process and on the two-sided Lanczos method, respectively, which become very efficient when combined with multishift solvers. Alternatively, in the variant based on the two-sided Lanczos method the sign function can be evaluated directly. We present numerical results which compare the efficiencies of a restarted Arnoldi-based method and the direct two-sided Lanczos approximation for various lattice sizes. We also show that our new methods gain substantially when combined with deflation.
MSC:
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81V05 | Strong interaction, including quantum chromodynamics |
| 82B30 | Statistical thermodynamics |
| 81Q12 | Nonselfadjoint operator theory in quantum theory including creation and destruction operators |
| 81T80 | Simulation and numerical modelling (quantum field theory) (MSC2010) |
| 81-08 | Computational methods for problems pertaining to quantum theory |
Keywords:
overlap Dirac operator; quark chemical potential; sign function; non-Hermitian matrix; iterative methodsSoftware:
mftoolboxReferences:
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