Doublon-only Sampling via `NExUpdatePath=6`

[tmisawa]

Summary

This change adds a new update path, NExUpdatePath=6, for real-space VMC sampling in a doublon-only Hilbert sector.

• Allowed on each site: (n_up, n_dn) = (1,1) (doublon) or (0,0) (empty)
• Local MC move: pair hopping only (move up/down together from one site to another)

For the actual implementation, see the following branch:

https://github.com/issp-center-dev/mVMC/tree/only_doublon

Motivation

Some studies require variational calculations restricted to a doublon sector. This adds the doublon-side counterpart to existing spin-oriented update modes.

Usage

Set in modpara.def:

NExUpdatePath  6

Use Orbital (not OrbitalGeneral) in namelist.def.

Current Constraints (fail-fast)

The run stops at startup unless all are satisfied:

• 0 < Ne < Nsite
• NlocalSpin = 0 in locspn.def
• NBackFlowIdx = 0
• No RBM inputs
• No FSZ (OrbitalGeneral / iFlgOrbitalGeneral=1)

Validation

Normal

• Hubbard chain (6 sites, Ne=3) with NExUpdatePath=6 runs to completion and outputs physical quantities.

Invalid inputs (representative)

Case	Exit code	Representative error
Ne=0	1	NExUpdatePath=6 (doublon-only) requires Ne > 0.
Ne=Nsite	1	NExUpdatePath=6 (doublon-only) requires Ne < Nsite (need empty sites for pair hopping).
NLocalSpin>0	1	NExUpdatePath=6 (doublon-only) is not compatible with NLocalSpin > 0.
BackFlow enabled	1	Back Flow is not supported. (when built with _NOTBACKFLOW)
RBM enabled	1	NExUpdatePath=6 (doublon-only) is not compatible with RBM (current implementation).
FSZ enabled	1	NExUpdatePath=6 (doublon-only) is not compatible with iFlgOrbitalGeneral=1 (FSZ).

Notes

• We reserve NExUpdatePath=6 to avoid collision with our local tJ validation branch (path=4,5, unpublished).
• Depending on build options, BackFlow may fail with a generic error before the dedicated NExUpdatePath=6 check.

Files touched

• src/mVMC/readdef.c
• src/mVMC/vmcmake.c
• src/mVMC/vmcmake_real.c
• src/mVMC/locgrn.c
• src/mVMC/locgrn_real.c
• src/mVMC/include/vmcmake.h
• src/mVMC/include/global.h
• doc/en/source/expert.rst
• doc/ja/source/expert.rst