This is a (by far non-exhaustive) list of some references for the various ideas behind the code, sorted by year and author. They can be cited from the python doc-strings using the format [Author####]_. If you’re looking for introductory notes, don’t forget the ‘official’ [TeNPyNotes]. The review by [Schollwoeck2011] is also a classic introduction.

General reading


“Density matrix formulation for quantum renormalization groups” S. White, Phys. Rev. Lett. 69, 2863 (1992) doi:10.1103/PhysRevLett.69.2863, S. White, Phys. Rev. B 84, 10345 (1992) doi:10.1103/PhysRevB.48.10345


“The density-matrix renormalization group” U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005), arXiv:0409292 doi:10.1103/RevModPhys.77.259


“Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems” F. Verstraete and V. Murg and J.I. Cirac, Advances in Physics 57 2, 143-224 (2009) arXiv:0907.2796 doi:10.1080/14789940801912366


“Renormalization and tensor product states in spin chains and lattices” J. I. Cirac and F. Verstraete, Journal of Physics A: Mathematical and Theoretical, 42, 50 (2009) arXiv:0910.1130 doi:10.1088/1751-8113/42/50/504004


“The density-matrix renormalization group in the age of matrix product states” U. Schollwoeck, Annals of Physics 326, 96 (2011), arXiv:1008.3477 doi:10.1016/j.aop.2010.09.012


“Characterizing Topological Order by Studying the Ground States on an Infinite Cylinder” L. Cincio, G. Vidal, Phys. Rev. Lett. 110, 067208 (2013), arXiv:1208.2623 doi:10.1103/PhysRevLett.110.067208


“Entanglement and tensor network states” J. Eisert, Modeling and Simulation 3, 520 (2013) arXiv:1308.3318


“A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States” R. Orus, Annals of Physics 349, 117-158 (2014) arXiv:1306.2164 doi:10.1016/j.aop.2014.06.013

Related theory


“Quantum-Mechanical Position Operator in Extended Systems” R. Resta, Phys. Rev. Lett. 80, 1800 (1997) doi:10.1103/PhysRevLett.80.1800


“Condensed Matter Applications of Entanglement Theory” N. Schuch, Quantum Information Processing. Lecture Notes of the 44th IFF Spring School (2013) arXiv:1306.5551

Algorithm developments


“Density matrix renormalization group algorithms with a single center site” S. White, Phys. Rev. B 72, 180403(R) (2005), arXiv:cond-mat/0508709 doi:10.1103/PhysRevB.72.180403


“Tensor network decompositions in the presence of a global symmetry” S. Singh, R. Pfeifer, G. Vidal, Phys. Rev. A 82, 050301(R), arXiv:0907.2994 doi:10.1103/PhysRevA.82.050301


“Tensor network states and algorithms in the presence of a global U(1) symmetry” S. Singh, R. Pfeifer, G. Vidal, Phys. Rev. B 83, 115125, arXiv:1008.4774 doi:10.1103/PhysRevB.83.115125


“Strictly single-site DMRG algorithm with subspace expansion” C. Hubig, I. P. McCulloch, U. Schollwoeck, F. A. Wolf, Phys. Rev. B 91, 155115 (2015), arXiv:1501.05504 doi:10.1103/PhysRevB.91.155115


“Finding purifications with minimal entanglement” J. Hauschild, E. Leviatan, J. H. Bardarson, E. Altman, M. P. Zaletel, F. Pollmann, Phys. Rev. B 98, 235163 (2018), arXiv:1711.01288 doi:10.1103/PhysRevB.98.235163

Time evolution


“Time-Dependent Variational Principle for Quantum Lattices” J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pizorn, H. Verschelde, F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011), arXiv:1103.0936 doi:10.1103/PhysRevLett.107.070601


“Unifying time evolution and optimization with matrix product states” J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken, F. Verstraete, Phys. Rev. B 94, 165116 (2016), arXiv:1408.5056 doi:10.1103/PhysRevB.94.165116


“Time-evolution methods for matrix-product states” S. Paeckel, T. Köhler, A. Swoboda, S. R. Manmana, U. Schollwöck, C. Hubig, arXiv:1901.05824

Finite temperature


“Reducing the numerical effort of finite-temperature density matrix renormalization group calculations” C. Karrasch, J. H. Bardarson, J. E. Moore, New J. Phys. 15, 083031 (2013), arXiv:1303.3942 doi:10.1088/1367-2630/15/8/083031

One-dimensional systems


“Efficient Simulation of One-Dimensional Quantum Many-Body Systems” G. Vidal, Phys. Rev. Lett. 93, 040502 (2004), arXiv:quant-ph/0310089 doi:10.1103/PhysRevLett.93.040502


“Detection of symmetry-protected topological phases in one dimension” F. Pollmann, A. Turner, Phys. Rev. B 86, 125441 (2012), arXiv:1204.0704 doi:10.1103/PhysRevB.86.125441

Two-dimensional systems


“Fractional quantum Hall states at zero magnetic field” Titus Neupert, Luiz Santos, Claudio Chamon, and Christopher Mudry, Phys. Rev. Lett. 106, 236804 (2011), arXiv:1012.4723 doi:10.1103/PhysRevLett.106.236804


“Topological flat band models with arbitrary Chern numbers” Shuo Yang, Zheng-Cheng Gu, Kai Sun, and S. Das Sarma, Phys. Rev. B 86, 241112(R) (2012), arXiv:1205.5792, doi:10.1103/PhysRevB.86.241112


“Characterization and stability of a fermionic ν=1/3 fractional Chern insulator” Adolfo G. Grushin, Johannes Motruk, Michael P. Zaletel, and Frank Pollmann, Phys. Rev. B 91, 035136 (2015), arXiv:1407.6985 doi:10.1103/PhysRevB.91.035136