## DMC timestep bias asymptotic

General discussion of quantum Monte Carlo in electronic structure theory

### Re: DMC timestep bias asymptotic

In these cases, instead of fitting a+b.tau^(1/2)+c.tau... to the DMC energy, it might be better to fit (a+b.tau+c.tau^2)/(1+D.tau) to the energy against time step tau. This describes a crossover between two different linear bias regimes.

Best wishes,

Neil.
Neil Drummond

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### Re: DMC timestep bias asymptotic

Neil Drummond wrote:In these cases, instead of fitting a+b.tau^(1/2)+c.tau... to the DMC energy, it might be better to fit (a+b.tau+c.tau^2)/(1+D.tau) to the energy against time step tau. This describes a crossover between two different linear bias regimes.

Best wishes,

Neil.

woohoo excellent!

timestep bias
be2.png (7.78 KiB) Viewed 3613 times

but this is very bad news for me, because the correlation length is where the red line, and 1/(3*Z^2) is where the black.
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### Re: DMC timestep bias asymptotic

Thanks for sending the graph. I think I'll stick to plane waves and pseudopotentials...

Best wishes,

Neil.
Neil Drummond

Posts: 82
Joined: Fri May 31, 2013 10:42 am
Location: Lancaster

### Re: DMC timestep bias asymptotic

Neil Drummond wrote:Thanks for sending the graph. I think I'll stick to plane waves and pseudopotentials...

Best wishes,

Neil.

Hello Neil

I want to make one very important comment for that fitting

E = (a+b.tau+c.tau^2)/(1+D.tau)

Where:
a is E at (tau->0)
b is slope at (tau->0)
c/d is slope at (tau->inf)

I interpolated all my data with this equation and got better or comparable to other eqs (within the error) results, but when the number of points at small tau is insufficient to determine the b value because error of b is compatible with its abs value, we can effectively set b=0 and then reinterpolate the data with simple equation. In this case we can nevertheless determine a with a small enough error and find out a parabolic-like dependence between E and tau at small tau.
This also explains many of the previously published E(tau) dependencies.

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### Re: DMC timestep bias asymptotic

Thanks very much for investigating this.

The slope at tau=0 is b-D.a, so setting b=0 doesn't get rid of the slope at tau=0 (but I can nevertheless believe that setting b=0 gives a reasonable fitting function for the situation you describe).

Best wishes,

Neil.
Neil Drummond

Posts: 82
Joined: Fri May 31, 2013 10:42 am
Location: Lancaster

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