• 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. It can be executed with ratApprox input.dat out.rational

• The input file input.dat should be structured as

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

• Example File

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 (\({\sqrt{m_{l}\times m_{s}}}\))
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 \(\frac{m_{s}}{m_{l}}\)