What is the best way to implement symmetrizations?

[evanberkowitz]

For example, when µ=0 on bipartite lattices, phi --> –phi? Let's say I want to measure on both, which I know is allowed because of https://arxiv.org/abs/1812.09268 IV.B

[luutom]

Adding to this, under the flow, the generalization of this symmetry is Re phi --> - Re phi with the corresponding phase changing as Im S --> - Im S. I acutally think we should implement this.

[jl-wynen]

How do you handle autocorrelations? Do you measure on phi_i and then on -phi_i or do you measure on all phi and then on all -phi?
In the former approach each measurement would consist of pairs of fully correlated points which would be removed by binning. In the latter, there would be strange correlations of length size_of_dataset / 2.
Or do you combine measurements on phi_i and -phi_i and never treat them as individual results?

[evanberkowitz]

Let's say that symmetry means coming with the same weight = Re S. Then I think you can take the phase-weighted average and ascribe it the average weight. It's like doing a markov chain on symmetry classes of configurations, rather than configurations themselves.

If they DON'T come with the same weight=Re S, I'd have to think. There is almost certainly a configuration-by-configuration reweighting procedure but I don't know it off the top of my head.

I think, for example, when µ≠0 we're going to fall into that second case---finite µ is going to separate the weights of +phi and –phi.