QCDMeasurements.jl

Measurements for lattice QCD.

Lattice QCD is a well-established non-perturbative approach to solving the quantum chromodynamics (QCD) theory of quarks and gluons. Gauge field for gluons is treated by Gaugefields.jl. Pseudo fermion field for quarks is treated by LatticeDiracOperators.jl. It is important to measure physical observables from gauge fields. QCDMeasurements.jl is now the external package for measurements in Lattice QCD.

This is intended to use in LatticeQCD.jl and a code in a project JuliaQCD.

What this package can do:

This package has following functionarities

• Plaquette measurement.
• Polyakov loop measurement.
• Pion correlator measurement.
• Chiral condensate measurement.
• Topological charge measurement.
• Energy density measurement.
• Wilson loop measurement

Sample

using QCDMeasurements
using Gaugefields
function test()
    println("SU3test")
    NX = 4
    NY = 4
    NZ = 4
    NT = 4
    Nwing = 0
    Dim = 4
    NC = 3

    U = Initialize_4DGaugefields(NC,Nwing,NX,NY,NZ,NT,condition = "cold")
    #U = Initialize_Gaugefields(NC,Nwing,NX,NY,NZ,NT,condition = "hot",randomnumber="Reproducible")
    filename = "testconf.txt"
    L = [NX,NY,NZ,NT]
    load_BridgeText!(filename,U,L,NC)
    #=
    filename = "./conf_00000008.ildg"
    ildg = ILDG(filename)
    i = 1
    L = [NX,NY,NZ,NT]
    load_gaugefield!(U,i,ildg,L,NC)
    =#

    m_plaq = Plaquette_measurement(U)
    m_poly = Polyakov_measurement(U)

    plaq = get_value(measure(m_plaq,U))
    poly = get_value(measure(m_poly,U))
    println("plaq: $plaq")
    println("poly: $poly")

    m_energy = Energy_density_measurement(U)
    m_topo = Topological_charge_measurement(U)
    energy = get_value(measure(m_energy,U))
    topo = get_value(measure(m_topo,U))
    println("energy: $energy")
    println("topo: $topo")

    m_wilson = Wilson_loop_measurement(U,printvalues=true)
    wilsonloop = get_value(measure(m_wilson,U))
    println("wilson loop: ",wilsonloop)

    m_pion = Pion_correlator_measurement(U)
    m_pion_Staggered = Pion_correlator_measurement(U,fermiontype = "Staggered")
    m_pion_Wilson = Pion_correlator_measurement(U,fermiontype = "Wilson")
    pion = get_value(measure(m_pion,U))
    pion_s = get_value(measure(m_pion_Staggered,U))
    pion_w = get_value(measure(m_pion_Wilson,U))

    println("pion: $pion")
    println("pion correlator with Staggered fermion: $pion_s")
    println("pion correlator with  Wilson fermion: $pion_w")

    m_chiral_Staggered = Chiral_condensate_measurement(U,fermiontype = "Staggered")
    m_chiral_Wilson = Chiral_condensate_measurement(U,fermiontype = "Wilson")
    chiral_s = get_value(measure(m_chiral_Staggered,U))
    chiral_w = get_value(measure(m_chiral_Wilson,U))

    println("Chiral condensate with Staggered fermion: $chiral_s")
    println("Chiral condensatewith  Wilson fermion: $chiral_w")


    TC_methods = ["plaquette","clover"]
    m_topo = Topological_charge_measurement(U,TC_methods = TC_methods)
    g = Gradientflow(U)
    for itrj=1:100
        flow!(U,g)
        @time plaq_t = get_value(measure(m_plaq,U))
        @time poly = get_value(measure(m_poly,U))
        println("$itrj plaq_t = $plaq_t")
        println("$itrj polyakov loop = $(real(poly)) $(imag(poly))")

        @time topo = get_value(measure(m_topo,U))
        print("$itrj topological charge: ")
        for (key,value) in topo
            print("$key $value \t")
        end
        println("\t")
    end

end
test()

You can also use the dictionary type.

using QCDMeasurements
using Gaugefields
function SU3test()
    println("SU3test")
    NX = 4
    NY = 4
    NZ = 4
    NT = 4
    Nwing = 0
    Dim = 4
    NC = 3

    U = Initialize_4DGaugefields(NC,Nwing,NX,NY,NZ,NT,condition = "cold")
    #U = Initialize_Gaugefields(NC,Nwing,NX,NY,NZ,NT,condition = "hot",randomnumber="Reproducible")
    filename = "testconf.txt"
    L = [NX,NY,NZ,NT]
    load_BridgeText!(filename,U,L,NC)
    
    #=
    filename = "./conf_00000008.ildg"
    ildg = ILDG(filename)
    i = 1
    L = [NX,NY,NZ,NT]
    load_gaugefield!(U,i,ildg,L,NC)
    =#
    method = Dict()
    methodname = "Eigenvalue"
    method["methodname"] = methodname
    method["fermiontype"] = "Wilson"
    κ = 0.141139
    method["hop"] =  κ
    method["nev"] = 1 #number of eigenvalues
    m = prepare_measurement_from_dict(U,method)
    value,vectors = get_value(measure(m,U)) #eigenvalues and eigenvectors
    println("$methodname $value")
    

    method = Dict()
    methodname = "Pion_correlator"
    method["methodname"] = methodname
    method["fermiontype"] = "Staggered"
    method["mass"] = 1
    method["Nf"] = 4
    m = prepare_measurement_from_dict(U,method)
    value = get_value(measure(m,U))
    println("$methodname $value")

    method = Dict()
    methodname = "Pion_correlator"
    method["methodname"] = methodname
    method["fermiontype"] = "Wilson"
    method["hop"] = 1
    m = prepare_measurement_from_dict(U,method)
    value = get_value(measure(m,U))
    println("$methodname $value")


    methodsname = ["Plaquette","Polyakov_loop","Topological_charge","Chiral_condensate",
            "Pion_correlator","Energy_density","Wilson_loop","Eigenvalue"]
    method = Dict()
    for methodname in methodsname
        method["methodname"] = methodname
        m = prepare_measurement_from_dict(U,method)
        value = get_value(measure(m,U))
        if methodname == "Eigenvalue"
            println("$methodname $(value[1])")
        else
            println("$methodname $(value)")
        end
    end

end
SU3test()

Acknowledgment

If you write a paper using this package, please refer this code.

BibTeX citation is following

@article{Nagai:2024yaf,
    author = "Nagai, Yuki and Tomiya, Akio",
    title = "{JuliaQCD: Portable lattice QCD package in Julia language}",
    eprint = "2409.03030",
    archivePrefix = "arXiv",
    primaryClass = "hep-lat",
    month = "9",
    year = "2024"
}

and the paper is arXiv:2409.03030.