---
activity: ideate
artifact_kind: l3_active_idea
idea_statement: 'Explore vertex correction beyond Gamma=1 in qsGW: (a) one-shot vertex
  from LDA kernel, (b) cumulant expansion of G, (c) qsGW+DMFT hybrid, (d) self-consistent
  W with vertex'
motivation: qsGW systematically underestimates band gaps. Vertex corrections are the
  next term in Hedin hierarchy.
---
# Active Idea

## Idea Statement
Explore vertex correction directions beyond Gamma=1 in qsGW:
(a) One-shot vertex from LDA kernel
(b) Cumulant expansion of Green function
(c) qsGW+DMFT hybrid
(d) Self-consistent W with beyond-RPA vertex

## Motivation
qsGW with Gamma=1 systematically underestimates band gaps. Vertex corrections are the next term in the Hedin equation hierarchy.

## Prior Work (L2 Check)
To be queried.

## Risk Assessment
(a) cheap but may be insufficient.
(b) intermediate difficulty, formal justification.
(c) expensive, requires impurity solver.
(d) most complete but numerically challenging.

