Hi Jia,

the autocorrelation time has nothing to do with the inverse temperature. Its units are ‘Monte Carlo steps’. Having a large autocorrelation time means you need many Monte Carlo steps until you measure a new configuration, i.e. your updates are not efficient. If your autocorrelation time gets to be on the order of the simulation time (again, measured in Monte Carlo steps) your results will be unreliable.

The easiest way to overcome autocorrelation problems in the hybridization expansion is to increase the temperature. At high T your updates will be efficient, your autocorrelation times short, and your measurements reliable. Then gradually decrease T and see what happens to your results and errors.

Best,
Emanuel


On Sep 20, 2014, at 3:52 PM, Jia Chen <jiachenchem@gmail.com> wrote:

Dear Prof. Emanuel Gull,

Thank you very much for your help. Now, I have auto-correlation time for certain observables. I have one following question. If the auto-correlation time I got for a observable is larger than beta, is that a good indication of bad sampling, thus unreliable measurement? I am still not very used to imaginary time... Thank you again!

Cheers
Jia

On Sat, Sep 20, 2014 at 1:14 PM, Emanuel Gull <emanuel.gull@gmail.com> wrote:
Hi Jia,

the easiest way is to examine the hdf5 file (typically called sim.h5). ALPS estimates the autocorrelation times for all RealObservables and RealVectorObservables and writes them as ‘tau’ into the hdf5 file. h5ls -r sim.h5 will give you an overview of the hdf5 file. Find your observable under /simulation/results/name_of_observable/ and then have a look at the value of ‘tau’.

Some of the larger observables are stored as SimpleRealVectorObservables, and they do NOT have binning information stored (mainly for efficiency reasons). If you need autocorrelation times for those observables, you’ll have to change their type to RealVectorObservable.

Best,
Emanuel

On Sep 18, 2014, at 2:18 AM, Jia Chen <jc4165@columbia.edu> wrote:

> Dear all,
>
> I would like to know, if I can have auto-correlation time from hybridization expansion ctqmc simulations. I want to have an estimation of like, if it saturates with interaction parameters and if simulation is long enough. Appreciate your help.
>
> Best Wishes
> Jia




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Jia Chen