Browser electronic eigensolver
Browser electronic eigensolver
electron-solver.js builds the complex128 periodic-square KLM Hamiltonian, diagonalizes it and evaluates the occupied-state field. eigen-kernel.js contains the WebAssembly program as base64 so the Worker can initialize it without fetching a binary. It uses standard WebAssembly SIMD and has no imported functions, shared memory, threads, network or filesystem dependencies. Numerical results record the SHA-256 of the kernel. The dense Python reference is tools/variational_note_server.py::note_electrons. It uses src/ecnn4klm/util/exact.py::square_hamiltonian, the same matrix builder as klmsq2d_gc, with μ set to zero during matrix construction.
The only C++ wrapper is eigen-wrapper.cpp. Its column-major complex matrix stores two adjacent doubles per entry. Eigen’s SelfAdjointEigenSolver reduces a Hermitian matrix to tridiagonal form and computes both sorted eigenvalues and normalized eigenvectors. The JavaScript field is obtained by summing the three Pauli-matrix expectations over the occupied columns.
| Both electronic paths diagonalize the physical Hamiltonian H₀ and retain its levels ε. They compute λ = ε − μ to determine occupation and the grand potential. Summing occupied ε gives the electronic energy directly, so a large chemical potential cannot erase the physical spectrum through cancellation. For the lattice sizes exposed in the note, a filled band has energy Tr H₀ = 0 and its spin field vanishes. The zero-temperature boundary screen uses 8 × (2L²) × machine epsilon × max(max | λ | , max | ε | , | μ | ), including the absolute scales used in diagonalization and subtraction. |
periodic-electrons.js derives rectangular periods from the specified integer wavevectors and verifies that the proposed tile repeats exactly in the submitted spin array. A matching tile is solved at every allowed twist on the finite torus. All sectors contribute to the sorted spectrum and to the occupied-state field, whose local expectations carry a factor of one over the number of tiles. The zero-temperature resolution check uses the complete spectrum and the full dimension (2L²). Other textures use the original dense solver.
The published index.html embeds the executable modules, styles and third-party notices for both GitHub Pages and local offline use. The adjacent sources and checksum list support inspection and rebuilding.
To rebuild, download and extract unmodified Eigen 3.4.0 source (tar.gz SHA-256 8586084f71f9bde545ee7fa6d00288b264a2b7ac3607b974e54d13e7162c1c72). Use Zig 0.13.0 as the WASI C++ compiler and linker. The original Windows build used the ziglang-0.13.0-py3-none-win_amd64.whl distribution from PyPI (SHA-256 b64b2aa936ebbfeecfbb2611df331a5474edebe1246b98c2f56d6ae4d58b71fc). With these directories available, from the repository root run:
python -B notes/variational-ed/build-kernel.py --zig C:\path\to\zig.exe --eigen C:\path\to\eigen-3.4.0 --verify
--verify compares the rebuilt bytes to the shipped eigen-kernel.js. Omit it to regenerate that asset after an intentional source change. The compiler uses EIGEN_MPL2_ONLY, no fast-math flag and no parallel Eigen execution. The shipped program is 63,127 bytes, SHA-256 a8c32fc2be22f8be1f5fd259c0bf73b360fd52369c3ae1a3c45bccd0ffccb524.
Source notices and licenses for the unmodified Eigen and compiler runtime components are included in THIRD-PARTY-LICENSES.txt. Eigen is distributed primarily under the Mozilla Public License 2.0, and its corresponding sources are available at the pinned archive above. The rebuild script specifies both compiler stages and the complete list of exported symbols.