SuperfluidCorrelator and StringCorrelator #227
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…_functions.jl and wrote unit tests for SuperfluidCorrelator.
…d that it is diagonal
…ement for StringCorrelator
…ngCorrelator(0) where the mean filling is not 1. Updated test functions for StringCorrelator
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…unction definition
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…s in accordance with our Friday meeting
…rrelator,G2Correlator. Altered definition of StringCorrelator to return only the real part ofthe correlator function. The imaginary part is negligible when the mean filling is 1
…rect test functions worked as on local copy
| if M == N | ||
| return real(result) /M | ||
| end |
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It would be more efficient to avoid complex numbers altogether for integer filling factor. Probably the best way to do this is to branch at the beginning of the function on
if iszero(N % M) # %, remainder from integer division
n̄ = N÷M # integer division
... # phase sum is always integer; replace exp(pi * im) by (-1)
else
n̄ = N/M
... # complex algebra as you have now
end
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It is worth checking whether this will produce type-stable code. It should.
| d = mod(D, M) | ||
| v = onr(add) | ||
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| result = 0 |
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It looks a bit untidy to initialise result with an Int64 and then add ComplexFloat64s to it. Will this result in a type instability?
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The reccommended change to improve the efficiency of StringCorrelator was did indeed result in greater efficiency. This was checked using @benchmark for a range of inputs. I'm still unsure how to interpret the failure of the Benchmarks above though. |
| # function diagonal_element(::StringCorrelator{D}, add::SingleComponentFockAddress) where {D} | ||
| # M = num_modes(add) | ||
| # N = num_particles(add) | ||
| # n̄ = N/M | ||
| # d = mod(D, M) | ||
| # v = onr(add) | ||
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| # result = 0 | ||
| # for i in eachindex(v) | ||
| # phase_sum = sum( (v[mod1(k,M)] - n̄) for k in i:1:(i+d-1) ) | ||
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| # result += (v[i]- n̄) * exp(pi * im * phase_sum) * (v[mod1(i + d, M)]-n̄) | ||
| # end | ||
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| # if M == N | ||
| # return real(result) /M | ||
| # end | ||
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| # return result / M | ||
| # end |
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Please delete the commented code.
| function diagonal_element(::StringCorrelator{D}, add::SingleComponentFockAddress) where {D} | ||
| M = num_modes(add) | ||
| N = num_particles(add) |
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While this is fine for BoseFS, it will produce a type instability for the new OccupationNumberFS. It will be better to first check the type parameter N of SingleComponentFockAddress{N,M} to see if it might be missing and include that in the if condition to default back to the Complex case.
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When you say type instability for the OccupationNumberFS, you mean that the type of N can vary from all the different UInt sizes right? If so, I'm a little unsure of what to do. If you call num_particles() on say OccupationNumberFS(1,1,1), it returns something of type Int64. The return type is the same also for say BoseFS(1,1,1). I might be interpreting something wrong here.
Also regarding checking the type parameter N of a SingleComponentFockAddress{N,M}, is there a way to extract the type of N? I am unsure of how to do this
| if M == N | ||
| return real(result) /M | ||
| end | ||
| result += (v[i]- n̄) * exp(pi * im * phase_sum) * (v[mod1(i + d, M)]-n̄) |
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You are in the branch where phase_sum should be an integer and you have branched in order to avoid complex numbers. Have you tested and verified this function to return a real-valued number type?
I believe that you'd have to write it like this if you want to avoid complex numbers:
| result += (v[i]- n̄) * exp(pi * im * phase_sum) * (v[mod1(i + d, M)]-n̄) | |
| result += (v[i]- n̄) * (-1)^phase_sum * (v[mod1(i + d, M)]-n̄) |
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The code on line 381 on my local version looks like the correction suggestion that you made, not the red one. I think I changed this on a commit later but never pushed this commit
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Please push it then, such that we can see the latest version of the code.
| ```math | ||
| \\hat{C}_{\\text{string}}(d) = \\frac{1}{M} \\sum_{i}^{M} \\delta n_j (e^{i \\pi \\sum_{j \\leq k < j + d} \\delta n_k}) \\delta n_{j+d} | ||
| ``` | ||
| where ``\\delta \\hat{n}_j = \\hat{n}_j - \\bar{n}`` is the boson number deviation from the mean filling number. |
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Please add a definition for the mean particle number, i.e. \\bar{n}=N/M, where ...
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This has been altered.
Co-authored-by: Joachim Brand <j.brand@massey.ac.nz>
…achimbrand/Rimu.jl into feature/superfluid-correlator
Co-authored-by: mtsch <matijacufar@gmail.com>
Co-authored-by: mtsch <matijacufar@gmail.com>
…elator for real and complex return types to seperate helper functions. Co-authored-by: mtsch <matijacufar@gmail.com>
…achimbrand/Rimu.jl into feature/superfluid-correlator
Added extra type stability checks Co-authored-by: Joachim Brand <j.brand@massey.ac.nz>
Co-authored-by: Joachim Brand <j.brand@massey.ac.nz>
Co-authored-by: Joachim Brand <j.brand@massey.ac.nz>
Co-authored-by: Joachim Brand <j.brand@massey.ac.nz>
Co-authored-by: Joachim Brand <j.brand@massey.ac.nz>
joachimbrand
changed the title
Defined a string correlation function (StringCorrelator), from which the order parameter for the Haldane Insulator phase can be obtained. Completed documentation and tests for both StringCorrelator, as well as the previously existing SuperfluidCorrelator function.
New features
SuperfluidCorrelatoris a new type (<:AbstractHamiltonian) that represents an observable to measure superfluid correlations in a Bose Hubbard chain in real spaceStringCorrelatoris a new type (<:AbstractHamiltonian) that represents an observable to measure string correlations in an (extended) Bose Hubbard chain in real space