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carstenbauer / MonteCarlo.jl

Classical and quantum Monte Carlo simulations in Julia
https://carstenbauer.github.io/MonteCarlo.jl/dev/
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Average sign in DQMC #163

Open tpyang opened 2 years ago

tpyang commented 2 years ago

Hi Carsten,

Thank you for this wonderful code! Could I ask a quick question regarding the average sign?

I am trying the Hubbard model with repulsive U. Can I obtain the average sign from 1-mean(negative probability)?

ffreyer commented 2 years ago

I work with sign problem free models and I believe Carsten did so as well. Because of that we currently only have error logging for negative probabilities, which keeps track of the average magnitude rather than the mean. I think it would be fine to extend this to include a normal mean though. (Maybe also a normal min/max instead of the weird log min/max.) The code for this is in https://github.com/carstenbauer/MonteCarlo.jl/blob/master/src/flavors/DQMC/statistics.jl.

andrewkhardy commented 1 year ago

A related question to this: Do you have a good reference for the necessary conditions for sign-free QMC. I have a vague understanding of anti-unitary symmetries which is why you work with attractive Hubbard on a square lattice.

Would say a non-bipartite (like a triangular lattice) repulsive Hubbard be infeasible then? Especially if it was not time-reversal invariant?

ffreyer commented 1 year ago

I haven't looked into it since my master thesis and I never got a deep understanding of when a model is sign problem free and when it isn't. It's also an ongoing topic of research. Some of the more recent papers I looked at were: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.250601 https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.117.267002 https://arxiv.org/abs/1712.09412