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Gradient flow

The gradient flow equations can be integrated in two different ways:

  1. Using a fixed step-size integrator. In this approach one fixes the step size $\epsilon$ and the links are evolved from $V_\mu(t)$ to $V_\mu(t +\epsilon)$ using some integration scheme.
  2. Using an adaptive step-size integrator. In this approach one fixes the tolerance $h$ and the links are evolved for a time $t_{\rm end}$ (i.e. from $V_\mu(t)$ to $V_\mu(t +t_{\rm end})$) with the condition that the maximum error while advancing is not larger than $h$.

In general adaptive step size integrators are much more efficient, but one loses the possibility to measure flow quantities at the intermediate times $\epsilon, 2\epsilon, 3\epsilon,...$. Adaptive step size integrators are ideal for finite size scaling studies, while a mix of both integrators is the most efficient approach in scale setting applications.

Integration schemes

LatticeGPU.YM.wfl_euler — Function
    wfl_euler(::Type{T}, eps::T, tol::T)

Euler scheme integrator for the Wilson Flow. The fixed step size is given by eps and the tolerance for the adaptive integrators by tol.

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LatticeGPU.YM.zfl_euler — Function
    zfl_euler(::Type{T}, eps::T, tol::T)

Euler scheme integrator for the Zeuthen flow. The fixed step size is given by eps and the tolerance for the adaptive integrators by tol.

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LatticeGPU.YM.wfl_rk2 — Function
    wfl_rk2(::Type{T}, eps::T, tol::T)

Second order Runge-Kutta integrator for the Wilson flow. The fixed step size is given by eps and the tolerance for the adaptive integrators by tol.

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LatticeGPU.YM.zfl_rk2 — Function
    zfl_rk2(::Type{T}, eps::T, tol::T)

Second order Runge-Kutta integrator for the Zeuthen flow. The fixed step size is given by eps and the tolerance for the adaptive integrators by tol.

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LatticeGPU.YM.wfl_rk3 — Function
    wfl_rk3(::Type{T}, eps::T, tol::T)

Third order Runge-Kutta integrator for the Wilson flow. The fixed step size is given by eps and the tolerance for the adaptive integrators by tol.

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LatticeGPU.YM.zfl_rk3 — Function
    Zfl_rk3(::Type{T}, eps::T, tol::T)

Third order Runge-Kutta integrator for the Zeuthen flow. The fixed step size is given by eps and the tolerance for the adaptive integrators by tol.

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Integrating the flow equations

LatticeGPU.YM.flw — Function
    function flw(U, int::FlowIntr{NI,T}, ns::Int64, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace)

Integrates the flow equations with the integration scheme defined by int performing ns steps with fixed step size. The configuration U is overwritten.

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LatticeGPU.YM.flw_adapt — Function
    function flw_adapt(U, int::FlowIntr{NI,T}, tend::T, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace)

Integrates the flow equations with the integration scheme defined by int using the adaptive step size integrator up to tend with the tolerance defined in int. The configuration U is overwritten.

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Observables

LatticeGPU.YM.Eoft_plaq — Function
function Eoft_plaq([Eslc,] U, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace)

Measure the action density E(t) using the plaquette discretization. If the argument Eslc is given the contribution for each Euclidean time slice and plane are returned.

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LatticeGPU.YM.Eoft_clover — Function
function Eoft_clover([Eslc,] U, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace)

Measure the action density E(t) using the clover discretization. If the argument Eslc the contribution for each Euclidean time slice and plane are returned.

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LatticeGPU.YM.Qtop — Function
Qtop([Qslc,] U, gp::GaugeParm, lp::SpaceParm, ymws::YMworkspace)

Measure the topological charge Q of the configuration U using the clover definition of the field strength tensor. If the argument Qslc is present the contribution for each Euclidean time slice are returned. Only wors in 4D.

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