Literature

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

White1992

“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

Schollwoeck2005

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

Verstraete2009

“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

Cirac2009

“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

Schollwoeck2011

“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

CincioVidal2013

“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

Eisert2013

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

Orus2014

“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

Resta1997

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

Schuch2013

“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

White2005

“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

Singh2009

“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

Singh2010

“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

Hubig2015

“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

Hauschild2018

“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

Haegeman2011

“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

Haegeman2016

“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

Hubig2019

“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

Karrasch2013

“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

Vidal2004

“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

PollmannTurner2012

“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

Neupert2011

“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

Yang2012

“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

Grushin2015

“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