qlat.contract_field — Site-Level HVP Tensor Contraction

Source: qlat/qlat/contract_field.py

Note: Update this document when updating the source file.

Outline

  • contract_chvp_16(prop1, prop2) — full 16-component HVP field.

Overview

This module computes the conserved-point hadronic vacuum polarization (HVP) tensor with all 16 spin-color polarization combinations (mu * 4 + nu, where mu, nu ∈ {0,1,2,3}) at every lattice site.

Unlike contract_hvp.contract_chvp3_field which returns a LatData correlator on a single time slice, contract_chvp_16 returns a full lattice Field with 16 complex components per site. This is useful when spatial or point-by-point information is needed.

The underlying C++ function implements:

chvp_16(x, mu*4+nu) = tr(g5_herm(prop2(x)) * gamma[mu] * prop1(x) * gamma[nu])

where mu is the sink polarization and nu is the source polarization.

API Reference

contract_chvp_16(prop1, prop2)

Compute the 16-component HVP tensor field.

Parameter

Type

Description

prop1

Propagator4d

First propagator prop1_x_y.

prop2

Propagator4d

Second propagator prop2_x_y.

Returns: Field(ElemTypeComplexD) — field with 16 complex components per site, indexed as mu * 4 + nu.

Decorated with: @timer

Component Index Convention

Index

mu

nu

0

0

0

1

0

1

…

…

…

15

3

3

Examples

import qlat as q

q.begin_with_mpi([1, 1, 1, 4])

total_site = q.Coordinate([4, 4, 4, 8])
geo = q.Geometry(total_site)
rs = q.RngState("seed")

prop1 = q.Prop(geo)
prop1.set_rand(rs.split("prop1"))

prop2 = q.Prop(geo)
prop2.set_rand(rs.split("prop2"))

chvp = q.contract_chvp_16(prop1, prop2)
print(chvp.multiplicity)  # 16

q.end_with_mpi()