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TRIQS / triqs_0.x

DEPRECATED -- This is the repository of the older versions of TRIQS
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off-diagonal term of Weiss field #124

Closed hungdt closed 11 years ago

hungdt commented 11 years ago

Hello,

It seems to me that in the multiband problem with rotationally invariant interaction (spinflip=true), the TRIQS solver supports input Weiss field with off-diagonal terms e.g: 2-band model: G0['up'][1,2] != 0 and G0['down'][1,2] != 0

Am I correct? If so, how slow is it compared with the problem with only diagonal term, i.e. G0[spin][i,j] != 0 only if i==j ? In other word, what is the computational complexity with respect to \beta=1/T for the problem with off-diagonal term of the Weiss field?

Thank you very much, Hung

mferrero commented 11 years ago

@aichhorn, @leopo: looks like a question you guys know. In principle off-diagonal Weiss field are possible but I don't know if the multiband solver has this option?

aichhorn commented 11 years ago

Okay, these terms are possible, and interactions are correctly implemented for this case, solvermultiband.py can deal with that. The speed, however, is significantly lower than without these terms. Not only that you cannot use the Segment update any more, you also introduce off-diagonal hybridisation functions that result in a sign problem. Depending on this sign problem, the problem can even be unsolvable (in a reasonable amount of time), compared to the diagonal case. In the end, you have to try yourself if your problem at hand is still tractable with these terms or not, and how bad the sign problem is. A general statement from the distance is impossible to make.

hungdt commented 11 years ago

Thank you. I think you two answered my questions. I will try myself to see how bad the is. If it is too small, I will think of a way to eliminate the off-diagonal terms. Thanks, Hung