% Citation metadata for the tenkz package, staged into the upload archive.
% The version and date are checked against the \ProvidesPackage line of
% tex/tenkz/tikz-tensor-networks.sty by scripts/tenkz_ctan.py; do not edit them here alone.

@manual{tenkz,
  title        = {{tikz-tensor-networks}: tensor-network diagrams from a description of the
                  network},
  author       = {Lu, Sirui},
  year         = {2026},
  month        = {9},
  note         = {LaTeX package, version 0.8.0},
  url          = {https://github.com/LionSR/tenkz},
}

% =========================================================================
%  Foundational and modern tensor network references (matching TNLean)
% =========================================================================

@article{Cirac2021Matrix,
  author       = {Cirac, J. Ignacio and P{\'e}rez-Garc{\'i}a, David and Schuch, Norbert and Verstraete, Frank},
  title        = {Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, Theorems},
  journal      = {Reviews of Modern Physics},
  volume       = {93},
  number       = {4},
  pages        = {045003},
  year         = {2021},
  doi          = {10.1103/RevModPhys.93.045003},
  eprint       = {2011.12127},
  eprinttype   = {arxiv},
}

@article{PerezGarcia2007Matrix,
  author       = {P{\'e}rez-Garc{\'i}a, D. and Verstraete, F. and Wolf, M. M. and Cirac, J. I.},
  title        = {Matrix Product State Representations},
  journal      = {Quantum Information \& Computation},
  volume       = {7},
  number       = {5},
  pages        = {401--430},
  year         = {2007},
  eprint       = {quant-ph/0608197},
  eprinttype   = {arxiv},
}

@article{VerstraeteCirac2004PEPS,
  author       = {Verstraete, F. and Cirac, J. I.},
  title        = {Renormalization Algorithms for Quantum-Many Body Systems in Two and Higher Dimensions},
  journal      = {arXiv preprint},
  year         = {2004},
  eprint       = {cond-mat/0407066},
  eprinttype   = {arxiv},
}

@article{Cirac2017Annals,
  author       = {Cirac, J. Ignacio and P{\'e}rez-Garc{\'i}a, David and Schuch, Norbert and Verstraete, Frank},
  title        = {Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories},
  journal      = {Annals of Physics},
  volume       = {378},
  pages        = {100--149},
  year         = {2017},
  doi          = {10.1016/j.aop.2016.12.030},
  eprint       = {1606.00608},
  eprinttype   = {arxiv},
}

@article{Cirac2017MPU,
  author       = {Cirac, J. Ignacio and P{\'e}rez-Garc{\'i}a, David and Schuch, Norbert and Verstraete, Frank},
  title        = {Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants},
  journal      = {Journal of Statistical Mechanics: Theory and Experiment},
  volume       = {2017},
  number       = {8},
  pages        = {083105},
  year         = {2017},
  doi          = {10.1088/1742-5468/aa7e3b},
  eprint       = {1703.09188},
  eprinttype   = {arxiv},
}

@article{Molnar2018Normal,
  author       = {Moln{\'a}r, A. and Garre-Rubio, J. and P{\'e}rez-Garc{\'i}a, D. and Schuch, N. and Cirac, J. I.},
  title        = {Normal Projected Entangled Pair States Generating the Same State},
  journal      = {New Journal of Physics},
  volume       = {20},
  number       = {11},
  pages        = {113017},
  year         = {2018},
  doi          = {10.1088/1367-2630/aae94f},
  eprint       = {1804.04964},
  eprinttype   = {arxiv},
}

@article{Sanz2010Wielandt,
  author       = {Sanz, M. and P{\'e}rez-Garc{\'i}a, D. and Wolf, M. M. and Cirac, J. I.},
  title        = {A Quantum Version of {Wielandt}'s Inequality},
  journal      = {IEEE Transactions on Information Theory},
  volume       = {56},
  number       = {9},
  pages        = {4668--4673},
  year         = {2010},
  doi          = {10.1109/TIT.2010.2054562},
  eprint       = {0909.5347},
  eprinttype   = {arxiv},
}

@article{PerezGarcia2008String,
  author       = {P{\'e}rez-Garc{\'i}a, D. and Wolf, M. M. and Sanz, M. and Verstraete, F. and Cirac, J. I.},
  title        = {String Order and Symmetries in Quantum Spin Lattices},
  journal      = {Physical Review Letters},
  volume       = {100},
  number       = {16},
  pages        = {167202},
  year         = {2008},
  doi          = {10.1103/PhysRevLett.100.167202},
  eprint       = {0802.0447},
  eprinttype   = {arxiv},
}

@article{Schuch2010PEPS,
  author       = {Schuch, N. and Cirac, I. and P{\'e}rez-Garc{\'i}a, D.},
  title        = {{PEPS} as Ground States: Degeneracy and Topology},
  journal      = {Annals of Physics},
  volume       = {325},
  number       = {10},
  pages        = {2153--2192},
  year         = {2010},
  doi          = {10.1016/j.aop.2010.05.008},
  eprint       = {1001.3807},
  eprinttype   = {arxiv},
}

@article{DeLasCuevas2017Irreducible,
  author       = {De las Cuevas, G. and Cirac, J. I. and Schuch, N. and P{\'e}rez-Garc{\'i}a, D.},
  title        = {Irreducible Forms of Matrix Product States: Theory and Applications},
  journal      = {Journal of Mathematical Physics},
  volume       = {58},
  number       = {12},
  pages        = {121901},
  year         = {2017},
  doi          = {10.1063/1.4998639},
  eprint       = {1708.00029},
  eprinttype   = {arxiv},
}

@article{CiracGarreRubio2019OpenProblems,
  author       = {Cirac, J. I. and Garre-Rubio, J. and P{\'e}rez-Garc{\'i}a, D.},
  title        = {Mathematical Open Problems in Projected Entangled Pair States},
  journal      = {Revista Matem{\'a}tica Complutense},
  volume       = {32},
  number       = {3},
  pages        = {579--599},
  year         = {2019},
  doi          = {10.1007/s13163-019-00305-6},
  eprint       = {1903.09439},
  eprinttype   = {arxiv},
}

@article{Lu2026Autoformalization,
  author       = {Lu, S. and Tjoa, E. and Cirac, J. I.},
  title        = {Multi-agent Autoformalization of Tensor Network Theory},
  journal      = {arXiv preprint},
  year         = {2026},
  eprint       = {2607.07857},
  eprinttype   = {arxiv},
}

@article{Fannes1992Finitely,
  author       = {Fannes, M. and Nachtergaele, B. and Werner, R. F.},
  title        = {Finitely Correlated States on Quantum Spin Chains},
  journal      = {Communications in Mathematical Physics},
  volume       = {144},
  number       = {3},
  pages        = {443--490},
  year         = {1992},
  doi          = {10.1007/BF02099178},
}

@article{Schollwock2011DMRG,
  author       = {Schollw{\"o}ck, U.},
  title        = {The Density-Matrix Renormalization Group in the Age of Matrix Product States},
  journal      = {Annals of Physics},
  volume       = {326},
  number       = {1},
  pages        = {96--192},
  year         = {2011},
  doi          = {10.1016/j.aop.2010.09.012},
  eprint       = {1008.3477},
  eprinttype   = {arxiv},
}

@article{Orus2014Practical,
  author       = {Or{\'u}s, R.},
  title        = {A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States},
  journal      = {Annals of Physics},
  volume       = {349},
  pages        = {117--158},
  year         = {2014},
  doi          = {10.1016/j.aop.2014.06.013},
  eprint       = {1306.2164},
  eprinttype   = {arxiv},
}

@article{BridgemanChubb2017Handwaving,
  author       = {Bridgeman, J. C. and Chubb, C. T.},
  title        = {Hand-waving and Interpretive Dance: An Introductory Course on Tensor Networks},
  journal      = {Journal of Physics A: Mathematical and Theoretical},
  volume       = {50},
  number       = {22},
  pages        = {223001},
  year         = {2017},
  doi          = {10.1088/1751-8121/aa6dc3},
  eprint       = {1603.03039},
  eprinttype   = {arxiv},
}

@misc{Wolf2012Quantum,
  author       = {Wolf, Michael M.},
  title        = {Quantum Channels \& Operations: Guided Tour},
  year         = {2012},
  howpublished = {Lecture notes, Technical University of Munich},
  url          = {https://mediatum.ub.tum.de/doc/1099654/1099654.pdf},
}