wai-quantum 0.3.34: ground states of spin chains by DMRG, held to exact answers #159

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2026-10-05

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wai-quantum 0.3.34: ground states of spin chains by DMRG, held to exact answers ...

Claims that classical computers cannot simulate a material are claims about
entanglement; in one dimension the density-matrix renormalization group
usually can, with an error it reports. quantum_dmrg:

- Chain: nearest-neighbour spin-1/2 chains with real terms (XXZ Heisenberg in
  a field, transverse-field Ising), written as matrix-product operators (the
  finite-state machine of their terms).
- Two-site DMRG: Lanczos with full re-orthogonalisation for the lowest state
  of the effective Hamiltonian; truncation by the reduced density matrix's
  eigenvectors (max bond, weight cutoff); discarded weight and the
  entanglement entropy at every bond.
- symmetric_eigen: Householder tridiagonalisation and implicit QL
  (tred2/tql2), hypotenuses in-crate.
- Exact referees: Lanczos on the full 2^n space (to 22 sites), and the open
  transverse-field Ising chain as free fermions at any length
  (E0 = -1/2 sum Lambda_k, Lambda_k^2 the eigenvalues of (A-B)(A+B)).
- The effective Hamiltonian runs in blocks of rows across threads, each row in
  the same order: bit-identical at any thread count (a direct test fails on a
  1e-15 change to one block). The Lanczos tolerance is a setting (1e-8 by
  default; the energy error goes as its square).

Checked:
- the eigensolver reconstructs random symmetric matrices to 1e-12;
- the free-fermion energy equals exact diagonalisation (n = 4, 7, 10);
- DMRG equals exact diagonalisation to 1e-8 on Heisenberg and Ising chains;
- critical Ising: 1.1e-11 per site at 100 sites, 1.4e-11 at 200 against the
  exact energy; Heisenberg 100 sites: -44.127739250 at bond 64 and
  -44.127739889 at bond 128, converging from above;
- variational, monotone in sweeps, repeatable.

The cross-platform pin caught a pointer-width bug: the exact-diagonalisation
start vector multiplied in usize, which wraps differently on wasm32; it now
uses u64, and all 19 pins hold natively and under wasm32-wasip2.

CLI: wai-quantum dmrg [--chain ising|heisenberg] [-n] [--j --jz --h] [--bond]
[--sweeps] [--exact] [--json]. Example: dmrg_chain. CLI output byte-identical
natively and under WASI.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

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