About number of nsiw and wscut

[liu xinbao]

Dear all,

I am trying to calculate the superconducting transition temperature in imaginary axis using pade approx. When I set nsiw = 100, I got following results

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     Electron-phonon coupling strength =    0.2826915
     Estimated Allen-Dynes Tc =       0.0900327 K for muc =    0.10000
     Estimated BCS superconducting gap =       0.0000137 eV
     temp(  1) =   0.0500 K
     Solve anisotropic Eliashberg equations on imaginary-axis
     Total number of frequency points nsiw (      1 ) =    100
     Cutoff frequency wscut =     0.0027
     Size of allocated memory per pool : ~=    8.0666 Gb

as you can see, the memory usage is quite big, our server cannot afford bigger one.
But the wscut is still far lower than 10xE_{phonon}(the biggest phonon energy of my system is about 75meV), the estimated T_c is about 0.09K, it seems that there is some relationship between nsiw and temp(1) and wscut.
Since the memory usage is proportional to nswi, my question is how can I solve Migdal-Eliashberg Equation in imaginary axis with less than 10GB memory usage per pool (I have set etf_mem = 2 to reduce memory usage).
Any suggestion is welcome, thank you!

Best regards,
Xinbao,

[roxana]

Hi,

The Migdal-Eliashberg approach is very expensive to use at very low temperatures since the number of Matsubara frequencies increases as the temperature decreases. I personally never solved the equations for a temperature below 0.5K and most likely even if you afford to perform a calculation with 10GB memory per pool at 0.05K the algorithm will most likely crash. In principle, you can set the number of Matsubara frequencies in the input file using the flag nswi to keep your memory below 10GB per pool (in this case you don't set up wscut in the input file and it is estimated based on nswi).

A second alternative is to only solve the isotropic Migdal-Eliashberg equations (this only uses the Eliashberg spectral function and it is very cheap).

Best,
Roxana