Deborah.Esther.TraceRescaler

rescale_all_traces(
    trace_data::Dict{String, Vector{Vector{Float64}}},
    KappaF64::Float64,
    LatVol::Int
) -> Dict{String, Vector{Any}}

Rescale all input trace data by appropriate powers of the hopping parameter.

Arguments

• trace_data::Dict{String, Vector{Vector{Float64}}}: Dictionary containing raw trace data for each label.
• KappaF64::Float64: Hopping parameter $\kappa$ as a Float64.
• LatVol::Int: Lattice volume (e.g., $N_S^3 \times N_T$).

Returns

• Dict{String, Vector{Any}}: Dictionary with rescaled trace data.

rescale_trace(
    X_in::AbstractArray,
    Kappa::Float64,
    LatVol::Int,
    power::Int
) -> Vector{Float64}

Rescale the input trace data by a physical volume and hopping parameter factor.

This rescaling is performed in the context of research by Benjamin J. Choi, who uses measurement data provided by Hiroshi Ohno et al. (PoS(LATTICE2018)174). These data were generated with the BQCD HMC program (PoS(LATTICE2010)040 and EPJ Web Conf. 175, 14011 (2018)).

Here, as noted in PoS(LATTICE2010)040, Sec. 3 (p. 3), the original trace data is normalized by a factor of $12V$, where $V$ is the lattice volume. To make the normalization consistent with later analyses (e.g. Phys. Rev. D94, 114507 (2016), Eq. (4)), we rescale as follows:

\[\left[ \text{Tr} \, M^{-p} \right]_{\text{rescaled}} = 12 \, V \, \left( 2 \, \kappa \right)^{p} \, \left[ \text{Tr} \, M^{-p} \right]_{\text{in}}\]

where

• $V$ is the lattice volume,
• $\kappa$ is the hopping parameter,
• $p$ is the power.

Arguments

• X_in::AbstractArray : Raw input array (typically bootstrap samples).
• Kappa::Float64 : Hopping parameter.
• LatVol::Int : Lattice volume (e.g. $N_S^3 \times N_T$).
• power::Int : Power to which the hopping parameter is raised.

Returns

• Vector{Float64} : Rescaled trace data.