# Notice for the `Papers/` directory

This directory contains the arXiv LaTeX sources of the papers whose results
TNLean formalizes. They are included as reference material for the
formalization, with the permission of their authors. Copyright in these
works remains with their authors and, where applicable, their publishers.

**These files are not covered by the repository's license.** The top-level
`LICENSE` (Apache License 2.0) applies to the Lean code, the blueprint, and
the other original content of this repository, not to this directory. The
sources below carry arXiv's non-exclusive distribution license (or, for the
two oldest submissions, arXiv's assumed license for 1991-2003 submissions),
which grants no redistribution rights beyond arXiv itself. Do not reuse them
outside this repository without the authors' permission; the version of
record for each paper is the arXiv posting or the journal publication.

| arXiv ID | Title | Authors | arXiv license |
|---|---|---|---|
| [quant-ph/0608197](https://arxiv.org/abs/quant-ph/0608197) | Matrix Product State Representations | D. Pérez-García, F. Verstraete, M. M. Wolf, J. I. Cirac | assumed 1991-2003 |
| [0802.0447](https://arxiv.org/abs/0802.0447) | String Order and Symmetries in Quantum Spin Lattices | D. Pérez-García, M. M. Wolf, M. Sanz, F. Verstraete, J. I. Cirac | assumed 1991-2003 |
| [0909.5347](https://arxiv.org/abs/0909.5347) | A quantum version of Wielandt's inequality | M. Sanz, D. Pérez-García, M. M. Wolf, J. I. Cirac | non-exclusive-distrib 1.0 |
| [1001.3807](https://arxiv.org/abs/1001.3807) | PEPS as ground states: degeneracy and topology | N. Schuch, I. Cirac, D. Pérez-García | non-exclusive-distrib 1.0 |
| [1010.3732](https://arxiv.org/abs/1010.3732) | Classifying quantum phases using MPS and PEPS | N. Schuch, D. Pérez-García, I. Cirac | non-exclusive-distrib 1.0 |
| [1210.6613](https://arxiv.org/abs/1210.6613) | Frustration free gapless Hamiltonians for Matrix Product States | C. Fernández-González, N. Schuch, M. M. Wolf, J. I. Cirac, D. Pérez-García | non-exclusive-distrib 1.0 |
| [1606.00608](https://arxiv.org/abs/1606.00608) | Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories | J. I. Cirac, D. Pérez-García, N. Schuch, F. Verstraete | non-exclusive-distrib 1.0 |
| [1708.00029](https://arxiv.org/abs/1708.00029) | Irreducible forms of Matrix Product States: Theory and Applications | G. De las Cuevas, J. I. Cirac, N. Schuch, D. Pérez-García | non-exclusive-distrib 1.0 |
| [1804.04964](https://arxiv.org/abs/1804.04964) | Normal projected entangled pair states generating the same state | A. Molnár, J. Garre-Rubio, D. Pérez-García, N. Schuch, J. I. Cirac | non-exclusive-distrib 1.0 |
| [1903.09439](https://arxiv.org/abs/1903.09439) | Mathematical open problems in projected entangled pair states | J. I. Cirac, J. Garre-Rubio, D. Pérez-García | non-exclusive-distrib 1.0 |
| [2011.12127](https://arxiv.org/abs/2011.12127) | Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems | J. I. Cirac, D. Pérez-García, N. Schuch, F. Verstraete | non-exclusive-distrib 1.0 |