Exact Pseudofermion Action for Monte Carlo Simulation of Domain-Wall Fermion

We present an exact pseudofermion action for hybrid Monte Carlo simulation (HMC) of one-flavor domain-wall fermion (DWF), with the effective 4-dimensional Dirac operator equal to the optimal rational approximation of the overlap-Dirac operator with kernel $H=c{H}_w(1+d{\gamma }_5{H}_w{)}^{-1}$, where $c$ and $d$ are constants. Using this exact pseudofermion action, we perform HMC of one-flavor QCD, and compare its characteristics with the widely used rational hybrid Monte Carlo algorithm (RHMC). Moreover, to demonstrate the practicality of the exact one-flavor algorithm (EOFA), we perform the first dynamical simulation of the (1+1)-flavors QCD with DWF.