Pith. sign in

REVIEW 2 cited by

Matrix Product States: Symmetries and Two-Body Hamiltonians

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 0901.2223 v1 pith:WHJV4YSC submitted 2009-01-15 cond-mat.str-el quant-ph

M. Sanz , M. M. Wolf , D. Perez-Garcia , J. I. Cirac This is my paper · ORCID
classification cond-mat.str-elquant-ph
keywords invariantgrouphamiltoniansmatrixproductresultsstatestates
verification ladder T0 review T1 audit T2 compute T3 formal
0 comments
read the original abstract

We characterize the conditions under which a translationally invariant matrix product state (MPS) is invariant under local transformations. This allows us to relate the symmetry group of a given state to the symmetry group of a simple tensor. We exploit this result in order to prove and extend a version of the Lieb-Schultz-Mattis theorem, one of the basic results in many-body physics, in the context of MPS. We illustrate the results with an exhaustive search of SU(2)--invariant two-body Hamiltonians which have such MPS as exact ground states or excitations.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Symmetry-enforced minimal entanglement and correlation in quantum spin chains

    cond-mat.str-el 2024-12 conditional novelty 8.0 of 10

    For integer-spin chains with SO(3) and translation symmetry, the minimal Renyi entropy is the smaller of two explicit expressions, and zero correlation length is forbidden.

  2. Les Houches Lecture Notes on Tensor Networks

    cond-mat.str-el 2025-12 unverdicted novelty 2.0 of 10

    A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.

Pith tools