This is a (by far non-exhaustive) list of some references for the various ideas behind the code. They can be cited from the python doc-strings using the format [Author####]_. Within each category, we sort the references by year and author.
[TeNPyNotes] are lecture notes, meant as an introduction to tensor networks (focusing on MPS), and introduced TeNPy to the scientific community by giving examples how to call the algorithms in TeNPy. [TeNPySource] is the location of the source code, and the place where you can report bugs. [TeNPyDoc] is where the location is hosted online. [TeNPyForum] is the place where you can ask questions and look for help, when you are stuck with implementing something.
[Schollwoeck2011] is an extensive introduction to MPS, DMRG and TEBD with lots of details on the implementations, and a classic read, although a bit lengthy. Our [TeNPyNotes] are a shorter summary of the important concepts, similar as [Orus2014]. [Hubig2019] is a very good, recent review focusing on time evolution with MPS. The lecture notes of [Eisert2013] explain the area law as motivation for tensor networks very well. PEPS are for example reviewed in [Verstraete2009], [Eisert2013] and [Orus2014]. [Stoudenmire2011] reviews the use of DMRG for 2D systems. [Cirac2009] discusses the different groups of tensor network states.
[White1992] is the invention of DMRG, which started everything. [Vidal2004] introduced TEBD. [White2005] and [Hubig2015] solved problems for single-site DMRG. [McCulloch2008] was a huge step forward to solve convergence problems for infinite DMRG. [Singh2009], [Singh2010] explain how to incorporate Symmetries. [Haegeman2011] introduced TDVP, again explained more accessible in [Haegeman2016]. [Zaletel2015] is another standard method for time-evolution with long-range Hamiltonians. [Karrasch2013] gives some tricks to do finite-temperature simulations (DMRG), which is a bit extended in [Hauschild2018]. [Vidal2007] introduced MERA.
The following are referenced from somewhere in the algorithms.
The following are not physics-related, but are good to know if you want to work with TeNPy (or more generally Python).
- Barthel2020
"Optimized Lie–Trotter–Suzuki decompositions for two and three non-commuting terms" T. Barthel, Y. Zhang, Annals of Physics 418, 168165 (2020),
1901.0497410.1016/j.aop.2020.168165- CincioVidal2013
"Characterizing Topological Order by Studying the Ground States on an Infinite Cylinder" L. Cincio, G. Vidal, Phys. Rev. Lett. 110, 067208 (2013),
1208.262310.1103/PhysRevLett.110.067208- 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)
0910.113010.1088/1751-8113/42/50/504004- Eisert2013
"Entanglement and tensor network states" J. Eisert, Modeling and Simulation 3, 520 (2013)
1308.3318- Grushin2015
"Characterization and stability of a fermionic ν=1/3 fractional Chern insulator" A. G. Grushin, J. Motruk, M. P. Zaletel, and F. Pollmann, Phys. Rev. B 91, 035136 (2015),
1407.698510.1103/PhysRevB.91.035136- HDF5
"Hierarchical Data Format 5 (R)", https://portal.hdfgroup.org/display/HDF5/HDF5 A file format and library for saving data (including metadata). We use it through the python interface of the h5py <https://docs.h5py.org/en/stable/>, see
/intro/input_output.- 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),
1103.093610.1103/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),
1408.505610.1103/PhysRevB.94.165116- 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),
1711.0128810.1103/PhysRevB.98.235163- 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),
1501.0550410.1103/PhysRevB.91.155115- Hubig2019
"Time-evolution methods for matrix-product states" S. Paeckel, T. Köhler, A. Swoboda, S. R. Manmana, U. Schollwöck, C. Hubig,
1901.05824- 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),
1303.394210.1088/1367-2630/15/8/083031- McCulloch2008
"Infinite size density matrix renormalization group, revisited" I. P. McCulloch,
0804.2509- Murg2010
"Matrix product operator representations" V. Murg, J.I. Cirac, B. Pirvu, F. Verstraete, New J. Phys. 12 025012 (2010),
0804.3976,10.1088/1367-2630/12/2/025012- Neupert2011
"Fractional quantum Hall states at zero magnetic field" T. Neupert, L. Santos, C. Chamon, and C. Mudry, Phys. Rev. Lett. 106, 236804 (2011),
1012.472310.1103/PhysRevLett.106.236804- Orus2014
"A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States" R. Orus, Annals of Physics 349, 117-158 (2014)
1306.216410.1016/j.aop.2014.06.013- PollmannTurner2012
"Detection of symmetry-protected topological phases in one dimension" F. Pollmann, A. Turner, Phys. Rev. B 86, 125441 (2012),
1204.070410.1103/PhysRevB.86.125441- Resta1997
"Quantum-Mechanical Position Operator in Extended Systems" R. Resta, Phys. Rev. Lett. 80, 1800 (1997)
10.1103/PhysRevLett.80.1800- Schollwoeck2011
"The density-matrix renormalization group in the age of matrix product states" U. Schollwoeck, Annals of Physics 326, 96 (2011),
1008.347710.1016/j.aop.2010.09.012- Schuch2013
"Condensed Matter Applications of Entanglement Theory" N. Schuch, Quantum Information Processing. Lecture Notes of the 44th IFF Spring School (2013)
1306.5551- Singh2009
"Tensor network decompositions in the presence of a global symmetry" S. Singh, R. Pfeifer, G. Vidal, Phys. Rev. A 82, 050301(R),
0907.299410.1103/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,
1008.477410.1103/PhysRevB.83.115125- Stoudenmire2010
"Minimally Entangled Typical Thermal State Algorithms" E.M. Stoudenmire, Steven R. White, 2010 New J. Phys. 12, 055026,
1002.130510.1088/1367-2630/12/5/055026- Stoudenmire2011
"Studying Two Dimensional Systems With the Density Matrix Renormalization Group" E.M. Stoudenmire, Steven R. White, Ann. Rev. of Cond. Mat. Physics, 3: 111-128 (2012),
1105.137410.1146/annurev-conmatphys-020911-125018- Suzuki1991
"General theory of fractal path integrals with applications to many-body theories and statistical physics", M. Suzuki, Journal of Mathematical Physics 32, 400 (1991);
10.1063/1.529425- TeNPyDoc
Online documentation, https://tenpy.readthedocs.io/
- TeNPyForum
Community forum for discussions, FAQ and announcements, https://tenpy.johannes-hauschild.de
- TeNPyNotes
"Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)" J. Hauschild, F. Pollmann, SciPost Phys. Lect. Notes 5 (2018),
1805.00055,10.21468/SciPostPhysLectNotes.5- TeNPySource
- 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)
0907.279610.1080/14789940801912366- Vidal2004
"Efficient Simulation of One-Dimensional Quantum Many-Body Systems" G. Vidal, Phys. Rev. Lett. 93, 040502 (2004),
quant-ph/031008910.1103/PhysRevLett.93.040502- Vidal2007
"Entanglement Renormalization" G. Vidal, Phys. Rev. Lett. 99, 220405 (2007),
cond-mat/0512165,10.1103/PhysRevLett.99.220405- White1992
"Density matrix formulation for quantum renormalization groups" S. White, Phys. Rev. Lett. 69, 2863 (1992)
10.1103/PhysRevLett.69.2863, S. White, Phys. Rev. B 84, 10345 (1992)10.1103/PhysRevB.48.10345- White2005
"Density matrix renormalization group algorithms with a single center site" S. White, Phys. Rev. B 72, 180403(R) (2005),
cond-mat/050870910.1103/PhysRevB.72.180403- 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),
1205.5792,10.1103/PhysRevB.86.241112- Zaletel2015
"Time-evolving a matrix product state with long-ranged interactions" M. P. Zaletel, R. S. K. Mong, C. Karrasch, J. E. Moore, F. Pollmann, Phys. Rev. B 91, 165112 (2015),
1407.183210.1103/PhysRevB.91.165112- conda
"conda package manger", https://docs.conda.io/en/latest/ A package and environment management system that allows to easily install (multiple version of) various software, and in particular python packages like TeNPy.
- git
"git version control system", https://git-scm.com A software which we use to keep track of changes in the source code.
- matplotlib
"Matplotlib", https://matplotlib.org/ A Python 2D plotting library. Some TeNPy functions expect
matplotlib.axes.Axesas arguments to plot into.- pip
"pip - the Python Package installer", https://pip.pypa.io/en/stable/ Traditional way to handle installed python packages with
pip install ...andpip uninstall ...on the command line.