Implemented disorder in the DCA Loop using the CT-AUX solver

[anirudha-mirmira]

Summary

Support DCA calculations for systems with static on-site disorder. The crux of the implementation is the idea that the addition of disorder configurations breaks the translational symmetry and requires the cluster problem to be solved with two real space indices (for the 2D case) instead of a single displacement index. The disorder averaging, which is carried out analogously to the CPA, restores translational symmetry, thereby allowing for the solution of the cluster problem with a single displacement and subsequently a single momentum index.

The flow proceeds as follows: Subsequent to the calculation of the cluster excluded G0(d), the real space indices are unfolded to get G0(r1,r2), the disorder configurations (box or binary) are added. This disordered_G0(r1,r2) is the bare line the walkers uses to walk the chains, followed by an two index M(r1,r2) accumulation. The resulting interacting G(r1,r2) is disorder averaged, folded back into a single displacement index G(d), transformed to G(k) and fed into the cluster finalization step.

CMake Options

The new code has an associated -DDCA_WITH_DISORDER=ON gate, which defines DISORDERED_G0 flag. The disorder parts are separated with #ifdef DISORDERED_G0 conditionals. The -DDCA_WITH_DISORDER=OFF flag results is identical to the clean code except in the places as noted below

Main differences from the DCA++ main branch

These are the changes to existing, shared code paths:

• g0_interpolation now uses the two r-index signature G0(r1, r2) in both the clean and
  disordered cases. : The clean code calculated a single index as subtract(r2,r1) in the g0_interpolation routines, which is now calculated after inputting both the indices separately;

• Fixed a latent divide-by-sign bug in local_G_k_w (used by computeErrorBars) in
  both branches: the get_accumulated_sign was used where the scalar accumulated
  get_accumulated_phase was intended (missed by the Feb-2023 Phase refactor).

• CMake files where a new CMake option DCA_WITH_DISORDER (OFF by default) defining DISORDERED_G0, plus a
  new DisorderParameters block (with MPI broadcast) and disorder-related parameter wiring.

Features

• Generates disorder configuration (equally weighted) using random numbers picked from a binary or box distribution. Additionally, in the binary case, a unique-configs: true parameter allows for the generation of strictly unique configurations
• The disorder generation works even in the MPI case with a broadcasted seed, which ensures each rank solves the QMC for an identically disordered ensemble.
• Error bars and stat tests: The disordered case generates a disorder averaged (translationally invariant) G_k_w and S_k_w per rank allowing calculation of error bars and statistical testing
• Input handling: A missing disorder block in the input is handled elegantly with fallback to the clean limit calculation. Improperly configured num-configurations: 0 is handled with a warning and calculation with a single configuration

Example disorder block in input

Disorder is configured by adding a disorder block to the run's JSON input. The presence of
the block is what enables the disorder flow; omit it for a clean run.

"disorder": {
  "distribution": "binary",
  "potential": 0.1,
  "density": 0.5,
  "num-configurations": 4,
  "unique-configs": false
}

• distribution - "binary" or "box" (any other value is a hard error).
• potential - disorder strength: V for binary (levels ±V/2), or the full box width W.
• density - fraction of sites at +V/2 for the binary distribution (ignored by box). For values away from 0.5, adjust-chemical-potential in the physics block should be false to prevent chemical potential adjustment from undoing the effect of the shifted average potential.
• num-configurations - number of disorder realizations in the ensemble (equal weights).
• unique-configs - if true, enforce distinct binary realizations (no-op for box).

Tests

Added and tested disorder tests gated on DCA_WITH_DISORDER AND NOT DCA_WITH_CUDA AND NOT DCA_WITH_HIP, which test the following:

• parameter parsing
• walker-reads-correct-G0
• accumulation and orientation of the r1,r2 unfolding
• full disorder loop
• two statistical tests (U=4 V=0 vs. clean ED reference; box+binary ensemble at V=0.1 - sanity checks).

Limitations

• CPU only. A DCA_WITH_DISORDER + CUDA/HIP configuration is a deliberate hard CMake error: the GPU version is not implemented. The common G0_interpolation in the GPU case has the original signature and the two index version is not implemented.
• Single particle quantities only - G4 averaging and two index handling is not implemented in the disorder path
• Static, site-local, spin-symmetric disorder only - The potential enters as a frequency-independent term applied identically to both spins. Bond/off-diagonal, frequency-dependent, and spin-dependent (magnetic) disorder are not supported.
• Two distributions only - Only binary and box are accepted; any other distribution
  value is a hard error.
• Optimization after profiling, etc. has not been carried out in the case of disorder

[anirudha-mirmira]

Commit f5a4f67 also resolves #364