• These files are specific to quark masses. to generate these follow the instructions : https://latticeqcd.github.io/SIMULATeQCD/03_applications/rhmc.html
  • A tool to generate rational approximation files written by K. Clark can be found in SIMULATeQCD/src/tools/rational_approx. One can find a document explainRatApprox.pdf by Q. Yuan explaining the idea behind the rational approximation for the fermion determinant, as well as some of the following notation. The makefile makeRatApprox will compile the executable ratApprox, which will generate you a rational approximation file for use with the rhmc of SIMULATeQCD. You can call it with ```shell ratApprox input.dat out.rational ``` The input file input.dat should be structured as ```C npff // Number of pseudo-fermion flavors y1 y2 mprec // Pre-conditioner mass (reduces the condition number in CG) mq order1 order2 lambda_low lambda_high precision
• exampleInput.dat

2

3
0
0
0.0652
14
12
0.004251039999999999
5.0
50

2
-2
0.0652
0.00241
14
12
5.8080999999999995e-06
5.0
160

2 # number of pseudo fermion flavours

• parameters for psf1(light quark pseudo fermion determinant)

3 #y1
0 # y2
0 # preconditioning mass for strange quark determinant
0.0783706 # m_s (strange quark mass) (m_quark)
14
12
0.00614195094436 # (m_s)^{2}
5.0 # \(\lambda_{max}\)
50 # precision

• parameters for psf1(light quark pseudo fermion determinant)

2 # y1
-2 # y2
0.01508242900218416 # preconditioning mass (sqrt(m_l * m_s))
0.0029026 # light quark mass (m_l)
14 # order 1
12 # order2
8.42508676e-06 # light quark mass squared
5.0 # \(\lambda_{max}\)
160 # precision

The pdf at SIMULATeQCD/src/tools/rational_approx/explainRatApprox.pdf will have the below findings using plots

• The error decreases linearly with respect to increase in degree of polynomial to be used for ratinal approximation.
• The error remains constant with respect to increase in precision for a chosen degree of polynomial.
• The error increases a bit for given degree of polynomial if we increase the ratio \(\frac{m_{s}}{m_{l}}\)