Abstract
Lattice QCD simulations at small lattice spacings and quark masses close to their physical values are technically challenging. In particular, the simulations can get trapped in the topological charge sectors of field space or may run into instabilities triggered by accidental near-zero modes of the lattice Dirac operator. As already noted in ref. [1], the first problem is bypassed if open boundary conditions are imposed in the time direction, while the second can potentially be overcome through twisted-mass determinant reweighting [2]. In this paper, we show that twisted-mass reweighting works out as expected in QCD with open boundary conditions and 2+1 flavours of O(a) improved Wilson quarks. Further algorithmic improvements are tested as well and a few physical quantities are computed for illustration.
Highlights
To be able to control the systematic errors in lattice QCD computations, simulations of lattices with spacing smaller than 0.05 fm and spatial extent of at least 4 fm have to be performed
The use of open boundary conditions and twisted-mass determinant reweighting in numerical lattice QCD is profitable from the point of view stability, efficiency and conceptual clarity
While open boundary conditions slightly complicate the physics analysis of the calculated correlation functions, there are currently no practical alternative ways to avoid the well-known ergodicity problems related to the emergence of the topological charge sectors in the continuum limit
Summary
To be able to control the systematic errors in lattice QCD computations, simulations of lattices with spacing smaller than 0.05 fm and spatial extent of at least 4 fm have to be performed. The formulation of lattice QCD proposed by Wilson [8] is adopted, with counterterms added to cancel the leading effects in the lattice spacing a [9,10]. This version of the lattice theory has many desirable properties and is relatively easy to simulate. At fixed gauge coupling and quark masses, near-zero modes tend to be less frequent the larger the lattice volume V is, because the width of the distribution of the lowest eigenvalue of the Dirac operator decreases approximately like V −1/2 [12,13,14,15,16,17]. All simulations reported in this paper were performed using the publicly available openQCD program package [21]
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