Density Matrix Renormalization Group (DMRG) L1-322

Quantum MechanicsMatrix-product-state ground statesδ=10 · hardL_DAG = 3.8📋 Stub — not mineable

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Unclaimed Principle — open for contribution

This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.

To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.

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Forward model E

∣ P s i >= s u m T r [M^{s_{1}} .. M^{s_{L}}] ∣ s_{1} .. s_{L} >; minimi z e < P s i ∣ H ∣ P s i > i t er a t i v e l y

DMRG: sweep-based variational optimization of matrix product states (MPS); exact for 1D, powerful for quasi-1D.

L-DAG

E.MPO_hamiltonian -> O.regularize -> O.gs_energy

E.MPO_hamiltonianO.regularizeO.gs_energy

Well-posedness W

Existence:: true
Uniqueness:: true
Stability:: conditional
κ:: 2000

Exponential precision with bond dimension M in 1D; 2D DMRG limited by transverse correlation length.

Solvability C

Solver class:: ITensor, Block2, SyTen; DMRG with QN symmetries
Convergence rate q:: 2
Complexity:: principle-dependent

Specs (0)

No L2 specs registered yet for this principle.