qlat.gauge_action — Gauge Action Parameters

Source: qlat/qlat/gauge_action.pyx

Note: Update this document when updating the source file.

Outline

  1. Overview

  2. GaugeAction Class

  3. Examples

Overview

gauge_action defines the GaugeAction class, a lightweight container for the parameters that specify a lattice gauge action. In the standard Wilson formulation the action is parameterised by a single coupling beta; adding a rectangle term introduces a second parameter c1 (improved actions such as Iwasaki or DBW2).

The stored parameters are consumed by the HMC routines in qlat.hmc (e.g. gf_hamilton_node, set_gm_force) to evaluate the gauge Hamiltonian and its molecular-dynamics force.

import qlat as q

q.begin_with_mpi([[1, 1, 1, 1]])

ga = q.GaugeAction(5.5)          # Wilson action, beta=5.5
print(ga.beta())                 # 5.5
print(ga.c1())                   # 0.0

q.end_with_mpi()

GaugeAction Class

Constructor

GaugeAction(beta: float, c1: float = 0.0)

Parameter

Type

Default

Description

beta

float

—

Inverse gauge coupling (6 / g^2)

c1

float

0.0

Coefficient of the rectangle (improvement) term

  • c1 = 0.0 gives the standard Wilson plaquette action.

  • c1 = -0.331 corresponds to the Iwasaki action (the C++ default).

ga_wilson  = q.GaugeAction(6.0)            # pure Wilson
ga_iwasaki = q.GaugeAction(2.62, -0.331)   # Iwasaki improved

Methods

beta() -> float

Return the inverse gauge coupling parameter.

c1() -> float

Return the rectangle-term coefficient.

Examples

Basic Usage

import qlat as q

size_node_list = [
    [1, 1, 1, 1],
]

q.begin_with_mpi(size_node_list)

ga = q.GaugeAction(5.5, -0.331)
print(f"beta = {ga.beta()}")     # 5.5
print(f"c1   = {ga.c1()}")       # -0.331

# Copy via @=
ga2 = q.GaugeAction(0.0)
ga2 @= ga
print(f"ga2 beta = {ga2.beta()}")  # 5.5

q.end_with_mpi()

Gauge Hamiltonian with GaugeAction

import qlat as q

size_node_list = [
    [1, 1, 1, 1],
]

q.begin_with_mpi(size_node_list)

total_site = q.Coordinate([4, 4, 4, 8])
geo = q.Geometry(total_site)
rs = q.RngState("seed")
gf = q.GaugeField(geo)
gf.set_rand(rs.split("gf-init"), 0.5, 10)
gf.unitarize()

ga = q.GaugeAction(6.0)
h = q.gf_hamilton_node(gf, ga)
print(f"gauge Hamiltonian (node) = {h}")

q.end_with_mpi()