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SNEG 2.1

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@rokzitko rokzitko released this 01 Aug 11:23
· 4 commits to main since this release
v2.1
a6d5d39

SNEG 2.1 is a major release consolidating development from the 2024-2026 cycle.

SNEG is a Wolfram Language package for symbolic calculations with noncommuting second-quantization operators. It provides canonical operator ordering, Wick expansion, vacuum expectation values, occupation-number states, symmetry-adapted bases, and matrix representations.

New functionality

Multi-mode phonons

  • Added phononbasis[{N1, N2, ...}] for finite product bases with independent mode cutoffs.
  • Added mode-resolved phononnumber, phononplus, phononminus, and phononx operators.
  • Added phononid for constructing identities in truncated phonon spaces.
  • Extended ketbratensorproduct to an arbitrary number of factors.
  • Extended transformtoPH to construct fermion-phonon bases with multiple phonon modes.
  • Invalid mode indices now produce a diagnostic and return $Failed.

Symbolic sums

  • Added scalar[...] for explicitly marking numerical, non-operator expressions inside symbolic calculations.
  • Added Zeroonvac[...] for applying vacuum-annihilation rules to expressions, products, and symbolic sums.
  • Added differentiation, division, and conjugation support for symbolic sums.
  • Added FactorSeparableSumCustom and rulesumFactor for extracting factors separable from summation indices.
  • Added rulesumCollectKD and sumCollectSimplifyKD for collecting and simplifying Kronecker-delta contributions.
  • Improved nested-sum expansion, collection, denominator handling, and dummy-index renaming.
  • Fixed several cases of accidental index capture.

Projectors

  • Added projectorE and projectorO for projectors onto normalized |0> +/- |2> charge superpositions.
  • Added projectorEphi and projectorOphi for phase-dependent variants of these projectors.
  • Added shorthand forms accepting atomic operator names.

Bosonic ordering

Bosonic operators can now use:

ordering[op] = NONE

This disables automatic reordering. Contractions, normal ordering, vacuum expectation values, and Wick expansion have been updated to respect this convention.

Operator algebra and Wick evaluation

  • Corrected ordering between different fermion heads using EMPTY, SEA, and NONE conventions.
  • Each fermionic operator is now classified according to its own creation or annihilation convention during cross-head ordering.
  • NONE now acts as an absolute no-reordering barrier.
  • Different fermion heads retain vanishing canonical anticommutators.
  • Corrected vacuum expectation values for different fermion heads under SEA ordering.
  • Extended Majorana anticommutators to multiple indices and different Majorana heads.
  • Corrected Majorana-Grassmann anticommutation and Berezin-integration signs.
  • Preserved Grassmann coefficients in all vacuum-expectation-value and Wick implementations.
  • Corrected symbolic contractions involving NONE ordering.
  • Corrected bosonic and mixed boson-fermion Wick-pairing signs.
  • Fixed Wick evaluation for single bosonic operators.
  • Corrected commutators between different spin-operator heads.
  • Preserved symbolic operator declarations through conjugation and repeated conjugation.

States and basis construction

  • Improved ap so that it is linear in operator arguments while preserving the final state argument.
  • Improved handling of zero states during operator application and spin lowering.
  • Corrected Fock-space dimensions for spinless and arbitrary-spin fermionic operators. For example, a spin-3/2 fermionic orbital now produces the expected 16 states.
  • qsbasis and qsbasisvc now reject unsupported spinless and non-spin-1/2 inputs instead of returning invalid bases.
  • Empty charge-spin and spin-only sectors now return the valid vacuum sector.
  • Extended spinbasis to combinations of three or more arbitrary spins.
  • Preserved auxiliary ket labels during tensor products, spin lowering, and scalar-product calculations.
  • Improved vc2ops for zero-mode bases and states containing auxiliary kets.
  • Improved symbolic orthogonalization so that potentially nonzero symbolic vectors are not discarded.

Matrix representations

The optimized matrixrepresentationvcfast and matrixrepresentationvcsparse implementations now handle:

  • Complex and prefactored basis states.
  • Superposition bases through a safe fallback.
  • Rectangular left and right bases.
  • States mapped outside the selected basis.
  • Symbolic and user-defined auxiliary-ket overlaps.

Regression tests compare optimized results against the general matrix-representation implementation.

Distribution and compatibility

SNEG can now be installed directly as a Wolfram paclet. Mathematica 12.1 or newer is required for paclet installation:

PacletInstall[
  "https://github.com/rokzitko/sneg/releases/latest/download/SNEG.paclet"
]

Load the package and check the installed version with:

Needs["sneg`"]
$SnegVersion

Both Needs["sneg"]andNeeds["Sneg"] are supported.

Manual source installation remains available for Mathematica 7 through 12.0. SNEG has been tested with Mathematica versions through 15.

The release contains versioned SNEG-2.1.paclet and stable SNEG.paclet assets.

Examples and testing

  • Added an example of bosonic displacement-operator algebra and Baker-Campbell-Hausdorff identities.
  • Added multi-mode phonon examples and regression tests.
  • Added dedicated tests for the exact-diagonalization utilities.
  • Expanded regression coverage for operator ordering, Wick expansion, symbolic sums, bases, projectors, matrix representations, Majorana operators, and Grassmann variables.

Links

Full Changelog: v2.0.24...v2.1

Assets 4
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