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Implement the Lanczos algorithm in q-space (Bloch basis) where momentum
conservation q1+q2=q_pert makes the 2-phonon sector block-diagonal,
reducing psi vector size and anharmonic computation cost by ~N_cell.
New files:
- Modules/QSpaceLanczos.py: Python class inheriting from DL.Lanczos with
Hermitian Lanczos iteration, Bloch-transformed ensemble, q-pair mapping,
and correct PG symmetry construction (Cartesian rotations from spglib
fractional coords, manual atom permutation with lattice reduction)
- Modules/tdscha_qspace.jl: Julia extension for q-space ensemble averaging
with separate D3/D4 functions and acoustic mode masking
- tests/test_qspace/test_qspace_lanczos.py: Test comparing q-space vs
real-space Green functions (match within 2.4e-7 relative error)
Key fixes during development:
- Convert spglib rotations from crystal to Cartesian coords via M@R@M^{-1}
- Replace CC.symmetries.GetIRT (gives wrong atom permutations for some
symmetries) with manual modular lattice reduction
- Include translation in Bloch phase: exp(-2πi q'·L) where L=Rτ+t-τ'
- Mask acoustic modes (ω<1e-6) in f_Y, f_psi, and chi factors
Also includes the translational projection optimization in DynamicalLanczos
(O(n^2) permutations instead of O(n^3) matmuls for gamma_only).
Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
New usage guide section covering the QSpaceLanczos workflow (perturbation setup, mode looping, when to prefer q-space over real-space) and a new API reference page with auto-generated docs via mkdocstrings. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
Computes the anharmonic phonon spectral function at the Brillouin zone boundary (X point) for SnTe using the Q-space Lanczos algorithm with the pre-existing test ensemble. Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
which should solve the free energy Hessian in q space correctly. Right now, it seems to work extremely well, except for 1 q point in the test, where none of the algorithms seems to converge. We need to investigate the issue.
We fixed a nasty hermitian conjugation in Q points not related to themselves by the inversion symmetries. These q-points are not hermitian, so the Lanczos was failing in them due to a mismatch between row-major and column-major transposition done in julia vs python. This is fixed and now it seems to work properly. Still an issue on IR prefactor and convergence of the bicg for that q != -q + G points is present to be fixed (its is only a convergence issue, as by explicitly computing the full L matrix and inverting produces the correct result, and also the standard Lanczos with no-mode-mixing produces the correct results).
Documents the q-space free energy Hessian with usage examples, performance comparison table, and deep-dive on the algorithm (static Liouvillian, q-space block diagonality, acoustic mode handling, Hermiticity enforcement, symmetry reduction). Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
…nd q-space Lanczos This test verifies that the IR perturbation modulus matches exactly between DynamicalLanczos and QSpaceLanczos after fixing the double mass scaling and missing supercell factor in QSpaceLanczos.prepare_ir. The test: 1. Creates ASR-satisfying effective charges (+I for first atom, -I for second) 2. Compares perturbation_modulus for all three polarization directions 3. Uses existing SnTe test data with 2×2×2 supercell
- Implemented prepare_raman() method in QSpaceLanczos with support for:
- Polarized Raman (pol_vec_in, pol_vec_out)
- Unpolarized Raman components (indices 0-6 with correct prefactors)
- Mixed Raman tensor components
- Implemented prepare_unpolarized_raman() method for raw components
without prefactors (matching parent class interface)
- Modified prepare_perturbation_q() to support add parameter for
cumulative perturbations (needed for unpolarized Raman)
- Added comprehensive test test_raman_modulus.py that verifies:
- Perturbation modulus consistency between real-space and q-space
Lanczos for all polarized Raman components (xx, xy, yy, zz)
- Consistency for all 7 unpolarized Raman components
- Tests use dummy Raman tensor that satisfies translation invariance
- Fixed test setup to ensure Raman tensor is properly attached to
ens.current_dyn (used by Lanczos constructor) rather than ens.dyn_0
All tests pass, confirming the q-space implementation matches the
real-space implementation for Raman perturbations.
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We can use an efficient implementation of the Q-space Lanczos for computing the Hessian.
This is now implemented and working.