Quantum

Exhaustive Construction of Generalized Parent Hamiltonians for Matrix Product States

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 03/11/2026, 08:58:24 UTC.

Briefings

A 2026 arXiv preprint presents an exhaustive construction of generalized parent Hamiltonians for matrix product states (MPS), extending beyond conventional frustration-free models by allowing non-Hermitian telescoping terms. The study derives a local tensor equation linking inequivalent Hamiltonian classes to the MPS transfer matrix spectrum, revealing connections to non-Abelian symmetries and zero correlation length. The work also extends the framework to block-injective MPS, offering a systematic bridge between Hamiltonian structure and local quantum state properties.

Key points

• The study develops an exhaustive construction of generalized parent Hamiltonians for matrix product states (MPS), extending beyond conventional frustration-free models by allowing non-Hermitian telescoping terms that cancel out with periodic boundary conditions.
• A local tensor equation establishes a correspondence between inequivalent classes of generalized parent Hamiltonians and the MPS transfer matrix spectrum, linking Hamiltonian structure to local quantum state properties.

Context

Recent results on quantum many-body scars revealed that standard parent Hamiltonian constructions do not exhaust all possible Hamiltonians hosting a given MPS as an eigenstate. This work fills that gap by providing a systematic framework for generalized parent Hamiltonians, offering a bridge between Hamiltonian structure and local quantum state properties.

Limitations

The evidence is an arXiv preprint (arXiv:2611.00203v1) from November 2026, indicating preprint status and potential uncertainty. The scope is limited to translation-invariant MPS and block-injective MPS, with no additional background or experimental validation provided in the source.

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