[Hadstruct] Lanczos for ground state energy

[Joseph Karpie]

I have made a little more progress for the curious. First, taking only the real component is quite important. It stabilizes the complexity of the evalues significantly of course. I now take the real evalues and those that pass a very stringent CW test. For comparing to the effective mass, I take the E_0 from all remaining evalues whose jackknife samples are within the plot windows. You can see them plotted between an estimate of mean/error from standard deviation and from a maybe still incorrect 60% confidence window the authors suggest.

With the larger momentum pz=2,3 where we may have wished we used momentum smearing, you can begin to see the advantage creep in. By tmax=21, the effective mass is lost, but the Lanczos result sometimes is quite stable. There are still occasional cases you can see where the spread of the energies I get are quite wild. I haven't quite understood this yet.

It would be nice to discuss more what problems can come in from the noise or another problem which may bias this. Take a look athttps://arxiv.org/pdf/2407.21777 which as more details then the original.
________________________________
From: Joseph Karpie
Sent: Tuesday, August 20, 2024 5:05 PM
To: Joseph Karpie via Hadstruct <hadstruct at jlab.org>
Subject: Lanczos for ground state energy

Hey,

I have started testing the Lanczos idea for analyzing 2pt functions. I put basic formula and results into slides https://docs.google.com/presentation/d/1uaQpQhQawA7VGA--2cjqrsSCSPoB6ORvl2M9iQZD4dQ/edit?usp=sharing I'm happy with the results given how roughly they are made. In the plot of evalues, and considering physical evalues must be positive and real, you can tell most of them are garbage. I can explain the dirty filtering procedure I did tomorrow morning. I hope to actually do the more professional diagnostics in a next attempt. Unfortunately without going to longer times, this data doesn't actually reach the regime where the advantage is significant.

Best,
Joe

--
Joe Karpie
Pronouns: He/His/Him
Postdoctoral Fellow
Theoretical and Computational Physics Center
Jefferson Lab

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