Undecidability of the Spectral Gap

Cubitt, T. S., Perez-Garcia, D., & Wolf, M. M. (2015). Undecidability of the Spectral Gap. Nature, 528(7581), 207-211.

Type

Journal article

Intellectual base

Primary research

Year

2015

Volume

528

Issue

7581

Pages

207-211

DOI

10.1038/nature16059

DOI registrant

Springer Nature

Link

https://doi.org/10.1038/nature16059

Cited from

computer_science

Cited by

1 citation across 1 artifact.

Each citation links to the sentence it supports in the citing article.

Primes

• Computability
  • one structural reason the field works with constrained grammar classes. Physics. The spectral-gap problem for certain translation-invariant quantum lattice models is undecidable

    This sourceProves that whether certain translation-invariant quantum lattice models are gapped is undecidable.

    SupportedVerified against the work's full text

    Cubitt, Perez-Garcia and Wolf prove the undecidability the sentence states: they "construct families of quantum spin systems on a 2D lattice with translationally-invariant, nearest-neighbour interactions for which the spectral gap problem is undecidable". The sentence's restriction to certain models matches the paper's own restriction to constructed families rather than to all lattice Hamiltonians.

    “We construct families of quantum spin systems on a 2D lattice with translationally-invariant, nearest-neighbour interactions for which the spectral gap problem is undecidable.”

    Read by an automated reader; not a human review. How support was checked

Verification

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