Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

Chan, Garnet Kin-Lic; Keselman, Anna; Nakatani, Naoki; Li, Zhendong; White, Steven R.

doi:10.1063/1.4955108

Title: Matrix product operators, matrix product states, and ab initio density matrix renormalization group algorithms

Journal Article · Tue Jul 05 00:00:00 EDT 2016 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4955108· OSTI ID:1467831

Chan, Garnet Kin-Lic ^[1]; Keselman, Anna ^[2]; Nakatani, Naoki ^[3]; Li, Zhendong ^[1]; White, Steven R. ^[4]

Princeton Univ., NJ (United States). Dept. of Chemistry
Weizmann Inst. of Science, Rehovot (Israel). Dept. of Condensed Matter Physics; Univ. of California, Irvine, CA (United States). Dept. of Physics and Astronomy
Hokkaido Univ., Sapporo (Japan). Inst. for Catalysis
Univ. of California, Irvine, CA (United States). Dept. of Physics and Astronomy

Current descriptions of the ab initio density matrix renormalization group (DMRG) algorithm use two superficially different languages: an older language of the renormalization group and renormalized operators, and a more recent language of matrix product states and matrix product operators. The same algorithm can appear dramatically different when written in the two different vocabularies. Here, we carefully describe the translation between the two languages in several contexts. First, we describe how to efficiently implement the ab initio DMRG sweep using a matrix product operator based code, and the equivalence to the original renormalized operator implementation. Next we describe how to implement the general matrix product operator/matrix product state algebra within a pure renormalized operator-based DMRG code. Finally, we discuss two improvements of the ab initio DMRG sweep algorithm motivated by matrix product operator language: Hamiltonian compression, and a sum over operators representation that allows for perfect computational parallelism. The connections and correspondences described here serve to link the future developments with the past and are important in the efficient implementation of continuing advances in ab initio DMRG and related algorithms.

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Research Organization:: Princeton Univ., NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Simons Foundation

Grant/Contract Number:: SC0010530; SC0008624

OSTI ID:: 1467831

Alternate ID(s):: OSTI ID: 1260285

Journal Information:: Journal of Chemical Physics, Vol. 145, Issue 1; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 113 works

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References (90)

An algorithm for large scale density matrix renormalization group calculations Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 120, Issue 7 https://doi.org/10.1063/1.1638734	journal	February 2004
Hilbert space renormalization for the many-electron problem Li, Zhendong; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 144, Issue 8 https://doi.org/10.1063/1.4942174	journal	February 2016
Communication: A flexible multi-reference perturbation theory by minimizing the Hylleraas functional with matrix product states Sharma, Sandeep; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 141, Issue 11 https://doi.org/10.1063/1.4895977	journal	September 2014
Communication: Four-component density matrix renormalization group Knecht, Stefan; Legeza, Örs; Reiher, Markus The Journal of Chemical Physics, Vol. 140, Issue 4 https://doi.org/10.1063/1.4862495	journal	January 2014
An efficient matrix product operator representation of the quantum chemical Hamiltonian Keller, Sebastian; Dolfi, Michele; Troyer, Matthias The Journal of Chemical Physics, Vol. 143, Issue 24 https://doi.org/10.1063/1.4939000	journal	December 2015
Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group Chan, Garnet Kin-Lic; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 116, Issue 11 https://doi.org/10.1063/1.1449459	journal	March 2002
Parallelization strategies for density matrix renormalization group algorithms on shared-memory systems Hager, G.; Jeckelmann, E.; Fehske, H. Journal of Computational Physics, Vol. 194, Issue 2 https://doi.org/10.1016/j.jcp.2003.09.018	journal	March 2004
Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm Nakatani, Naoki; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 138, Issue 13 https://doi.org/10.1063/1.4798639	journal	April 2013
Entangled quantum electronic wavefunctions of the Mn4CaO5 cluster in photosystem II Kurashige, Yuki; Chan, Garnet Kin-Lic; Yanai, Takeshi Nature Chemistry, Vol. 5, Issue 8 https://doi.org/10.1038/nchem.1677	journal	June 2013
Density-matrix renormalization-group method in momentum space Xiang, T. Physical Review B, Vol. 53, Issue 16 https://doi.org/10.1103/PhysRevB.53.R10445	journal	April 1996
Construction of environment states in quantum-chemical density-matrix renormalization group calculations Moritz, Gerrit; Reiher, Markus The Journal of Chemical Physics, Vol. 124, Issue 3 https://doi.org/10.1063/1.2139998	journal	January 2006
Two-Dimensional Tensor Product Variational Formulation Nishino, T.; Hieida, Y.; Okunishi, K. Progress of Theoretical Physics, Vol. 105, Issue 3 https://doi.org/10.1143/PTP.105.409	journal	March 2001
Determining Factors for the Accuracy of DMRG in Chemistry Keller, Sebastian F.; Reiher, Markus CHIMIA International Journal for Chemistry, Vol. 68, Issue 4 https://doi.org/10.2533/chimia.2014.200	journal	April 2014
Quantum data compression, quantum information generation, and the density-matrix renormalization-group method Legeza, Ö.; Sólyom, J. Physical Review B, Vol. 70, Issue 20 https://doi.org/10.1103/PhysRevB.70.205118	journal	November 2004
Low entanglement wavefunctions: Low entanglement wavefunctions Chan, Garnet Kin-Lic Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 6 https://doi.org/10.1002/wcms.1095	journal	May 2012
Real-Time Evolution Using the Density Matrix Renormalization Group White, Steven R.; Feiguin, Adrian E. Physical Review Letters, Vol. 93, Issue 7 https://doi.org/10.1103/PhysRevLett.93.076401	journal	August 2004
A practical introduction to tensor networks: Matrix product states and projected entangled pair states Orús, Román Annals of Physics, Vol. 349 https://doi.org/10.1016/j.aop.2014.06.013	journal	October 2014
Ab initio quantum chemistry using the density matrix renormalization group White, Steven R.; Martin, Richard L. The Journal of Chemical Physics, Vol. 110, Issue 9 https://doi.org/10.1063/1.478295	journal	March 1999
Second-order perturbation theory with a density matrix renormalization group self-consistent field reference function: Theory and application to the study of chromium dimer Kurashige, Yuki; Yanai, Takeshi The Journal of Chemical Physics, Vol. 135, Issue 9 https://doi.org/10.1063/1.3629454	journal	September 2011
The density matrix renormalization group for ab initio quantum chemistry Wouters, Sebastian; Van Neck, Dimitri The European Physical Journal D, Vol. 68, Issue 9 https://doi.org/10.1140/epjd/e2014-50500-1	journal	September 2014
Quantum chemistry using the density matrix renormalization group Mitrushenkov, Alexander O.; Fano, Guido; Ortolani, Fabio The Journal of Chemical Physics, Vol. 115, Issue 15 https://doi.org/10.1063/1.1389475	journal	October 2001
Quasi-degenerate perturbation theory using matrix product states Sharma, Sandeep; Jeanmairet, Guillaume; Alavi, Ali The Journal of Chemical Physics, Vol. 144, Issue 3 https://doi.org/10.1063/1.4939752	journal	January 2016
The Density Matrix Renormalization Group in Quantum Chemistry Chan, Garnet Kin-Lic; Sharma, Sandeep Annual Review of Physical Chemistry, Vol. 62, Issue 1 https://doi.org/10.1146/annurev-physchem-032210-103338	journal	May 2011
Thermodynamic Limit of Density Matrix Renormalization Östlund, Stellan; Rommer, Stefan Physical Review Letters, Vol. 75, Issue 19 https://doi.org/10.1103/PhysRevLett.75.3537	journal	November 1995
High-performance ab initio density matrix renormalization group method: Applicability to large-scale multireference problems for metal compounds Kurashige, Yuki; Yanai, Takeshi The Journal of Chemical Physics, Vol. 130, Issue 23 https://doi.org/10.1063/1.3152576	journal	June 2009
The density matrix renormalization group algorithm on kilo-processor architectures: Implementation and trade-offs Nemes, Csaba; Barcza, Gergely; Nagy, Zoltán Computer Physics Communications, Vol. 185, Issue 6 https://doi.org/10.1016/j.cpc.2014.02.021	journal	June 2014
Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension Vidal, G. Physical Review Letters, Vol. 98, Issue 7 https://doi.org/10.1103/PhysRevLett.98.070201	journal	February 2007
Simulating strongly correlated quantum systems with tree tensor networks Murg, V.; Verstraete, F.; Legeza, Ö. Physical Review B, Vol. 82, Issue 20 https://doi.org/10.1103/PhysRevB.82.205105	journal	November 2010
Density-matrix renormalization-group algorithms with nonorthogonal orbitals and non-Hermitian operators, and applications to polyenes Chan, Garnet Kin-Lic; Van Voorhis, Troy The Journal of Chemical Physics, Vol. 122, Issue 20 https://doi.org/10.1063/1.1899124	journal	May 2005
The density-matrix renormalization group in the age of matrix product states Schollwöck, Ulrich Annals of Physics, Vol. 326, Issue 1 https://doi.org/10.1016/j.aop.2010.09.012	journal	January 2011
Improved parallelization techniques for the density matrix renormalization group Rincón, Julián; García, D. J.; Hallberg, K. Computer Physics Communications, Vol. 181, Issue 8 https://doi.org/10.1016/j.cpc.2010.03.018	journal	August 2010
Linear response theory for the density matrix renormalization group: Efficient algorithms for strongly correlated excited states Nakatani, Naoki; Wouters, Sebastian; Van Neck, Dimitri The Journal of Chemical Physics, Vol. 140, Issue 2 https://doi.org/10.1063/1.4860375	journal	January 2014
The ab-initio density matrix renormalization group in practice Olivares-Amaya, Roberto; Hu, Weifeng; Nakatani, Naoki The Journal of Chemical Physics, Vol. 142, Issue 3 https://doi.org/10.1063/1.4905329	journal	January 2015
Infinite time-evolving block decimation algorithm beyond unitary evolution Orús, R.; Vidal, G. Physical Review B, Vol. 78, Issue 15 https://doi.org/10.1103/PhysRevB.78.155117	journal	October 2008
Full-CI quantum chemistry using the density matrix renormalization group Daul, S.; Ciofini, I.; Daul, C. International Journal of Quantum Chemistry, Vol. 79, Issue 6 https://doi.org/10.1002/1097-461X(2000)79:6<331::AID-QUA1>3.0.CO;2-Y	journal	January 2000
Tree Tensor Network State with Variable Tensor Order: An Efficient Multireference Method for Strongly Correlated Systems Murg, V.; Verstraete, F.; Schneider, R. Journal of Chemical Theory and Computation, Vol. 11, Issue 3 https://doi.org/10.1021/ct501187j	journal	February 2015
The Density Matrix Renormalization Group Algorithm in Quantum Chemistry Marti, Konrad Heinrich; Reiher, Markus Zeitschrift für Physikalische Chemie, Vol. 224, Issue 3-4 https://doi.org/10.1524/zpch.2010.6125	journal	April 2010
Density matrix renormalization group calculations on relative energies of transition metal complexes and clusters Marti, Konrad H.; Ondík, Irina Malkin; Moritz, Gerrit The Journal of Chemical Physics, Vol. 128, Issue 1 https://doi.org/10.1063/1.2805383	journal	January 2008
Efficient Simulation of One-Dimensional Quantum Many-Body Systems Vidal, Guifré Physical Review Letters, Vol. 93, Issue 4 https://doi.org/10.1103/PhysRevLett.93.040502	journal	July 2004
N -Electron Valence State Perturbation Theory Based on a Density Matrix Renormalization Group Reference Function, with Applications to the Chromium Dimer and a Trimer Model of Poly( p -Phenylenevinylene) Guo, Sheng; Watson, Mark A.; Hu, Weifeng Journal of Chemical Theory and Computation, Vol. 12, Issue 4 https://doi.org/10.1021/acs.jctc.5b01225	journal	March 2016
Real-space parallel density matrix renormalization group Stoudenmire, E. M.; White, Steven R. Physical Review B, Vol. 87, Issue 15 https://doi.org/10.1103/PhysRevB.87.155137	journal	April 2013
Obtaining the two-body density matrix in the density matrix renormalization group method Zgid, Dominika; Nooijen, Marcel The Journal of Chemical Physics, Vol. 128, Issue 14 https://doi.org/10.1063/1.2883980	journal	April 2008
CheMPS2: A free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry Wouters, Sebastian; Poelmans, Ward; Ayers, Paul W. Computer Physics Communications, Vol. 185, Issue 6 https://doi.org/10.1016/j.cpc.2014.01.019	journal	June 2014
Matrix Product Density Operators: Simulation of Finite-Temperature and Dissipative Systems Verstraete, F.; García-Ripoll, J. J.; Cirac, J. I. Physical Review Letters, Vol. 93, Issue 20 https://doi.org/10.1103/PhysRevLett.93.207204	journal	November 2004
Spin-adapted density matrix renormalization group algorithms for quantum chemistry Sharma, Sandeep; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 136, Issue 12 https://doi.org/10.1063/1.3695642	journal	March 2012
Spin-adapted matrix product states and operators Keller, Sebastian; Reiher, Markus The Journal of Chemical Physics, Vol. 144, Issue 13 https://doi.org/10.1063/1.4944921	journal	April 2016
Analytic response theory for the density matrix renormalization group Dorando, Jonathan J.; Hachmann, Johannes; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 130, Issue 18 https://doi.org/10.1063/1.3121422	journal	January 2009
QC-DMRG study of the ionic-neutral curve crossing of LiF Legeza, O.; Roder, J.; Hess, B. A. Molecular Physics, Vol. 101, Issue 13 https://doi.org/10.1080/0026897031000155625	journal	July 2003
Controlling the accuracy of the density-matrix renormalization-group method: The dynamical block state selection approach Legeza, Ö.; Röder, J.; Hess, B. A. Physical Review B, Vol. 67, Issue 12 https://doi.org/10.1103/PhysRevB.67.125114	journal	March 2003
Optimizing Hartree-Fock orbitals by the density-matrix renormalization group Luo, H. -G.; Qin, M. -P.; Xiang, T. Physical Review B, Vol. 81, Issue 23 https://doi.org/10.1103/PhysRevB.81.235129	journal	June 2010
Exact solution (within a triple-zeta, double polarization basis set) of the electronic Schrödinger equation for water Chan, Garnet Kin-Lic; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 118, Issue 19 https://doi.org/10.1063/1.1574318	journal	May 2003
Multireference correlation in long molecules with the quadratic scaling density matrix renormalization group Hachmann, Johannes; Cardoen, Wim; Chan, Garnet Kin-Lic The Journal of Chemical Physics, Vol. 125, Issue 14 https://doi.org/10.1063/1.2345196	journal	October 2006
Low-energy spectrum of iron–sulfur clusters directly from many-particle quantum mechanics Sharma, Sandeep; Sivalingam, Kantharuban; Neese, Frank Nature Chemistry, Vol. 6, Issue 10 https://doi.org/10.1038/nchem.2041	journal	August 2014
Tensor product methods and entanglement optimization for ab initio quantum chemistry Szalay, Szilárd; Pfeffer, Max; Murg, Valentin International Journal of Quantum Chemistry, Vol. 115, Issue 19 https://doi.org/10.1002/qua.24898	journal	May 2015
Longitudinal static optical properties of hydrogen chains: Finite field extrapolations of matrix product state calculations Wouters, Sebastian; Limacher, Peter A.; Van Neck, Dimitri The Journal of Chemical Physics, Vol. 136, Issue 13 https://doi.org/10.1063/1.3700087	journal	April 2012
Quantum chemistry using the density matrix renormalization group II Mitrushenkov, A. O.; Linguerri, Roberto; Palmieri, Paolo The Journal of Chemical Physics, Vol. 119, Issue 8 https://doi.org/10.1063/1.1593627	journal	August 2003
Matrix product state applications for the ALPS project Dolfi, Michele; Bauer, Bela; Keller, Sebastian Computer Physics Communications, Vol. 185, Issue 12 https://doi.org/10.1016/j.cpc.2014.08.019	journal	December 2014
More π Electrons Make a Difference: Emergence of Many Radicals on Graphene Nanoribbons Studied by Ab Initio DMRG Theory Mizukami, Wataru; Kurashige, Yuki; Yanai, Takeshi Journal of Chemical Theory and Computation, Vol. 9, Issue 1 https://doi.org/10.1021/ct3008974	journal	December 2012
Density matrix renormalization group for ab initio Calculations and associated dynamic correlation methods: A review of theory and applications Yanai, Takeshi; Kurashige, Yuki; Mizukami, Wataru International Journal of Quantum Chemistry, Vol. 115, Issue 5 https://doi.org/10.1002/qua.24808	journal	October 2014
Class of ansatz wave functions for one-dimensional spin systems and their relation to the density matrix renormalization group Rommer, Stefan; Östlund, Stellan Physical Review B, Vol. 55, Issue 4 https://doi.org/10.1103/PhysRevB.55.2164	journal	January 1997
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems Verstraete, F.; Murg, V.; Cirac, J. I. Advances in Physics, Vol. 57, Issue 2 https://doi.org/10.1080/14789940801912366	journal	March 2008
Matrix product operator representations Pirvu, B.; Murg, V.; Cirac, J. I. New Journal of Physics, Vol. 12, Issue 2 https://doi.org/10.1088/1367-2630/12/2/025012	journal	February 2010
Finite-temperature density matrix renormalization using an enlarged Hilbert space Feiguin, Adrian E.; White, Steven R. Physical Review B, Vol. 72, Issue 22 https://doi.org/10.1103/PhysRevB.72.220401	journal	December 2005
State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve Chan, Garnet Kin-Lic; Kállay, Mihály; Gauss, Jürgen The Journal of Chemical Physics, Vol. 121, Issue 13 https://doi.org/10.1063/1.1783212	journal	October 2004
Orbital optimization in the density matrix renormalization group, with applications to polyenes and β-carotene Ghosh, Debashree; Hachmann, Johannes; Yanai, Takeshi The Journal of Chemical Physics, Vol. 128, Issue 14 https://doi.org/10.1063/1.2883976	journal	April 2008
Density matrix renormalisation group Lagrangians Chan, Garnet Kin-Lic Physical Chemistry Chemical Physics, Vol. 10, Issue 23 https://doi.org/10.1039/b805292c	journal	January 2008
Multireference linearized coupled cluster theory for strongly correlated systems using matrix product states Sharma, Sandeep; Alavi, Ali The Journal of Chemical Physics, Vol. 143, Issue 10 https://doi.org/10.1063/1.4928643	journal	September 2015
The Density Matrix Renormalization Group Algorithm in Quantum Chemistry Marti, Konrad Heinrich; Reiher, Markus Progress in Physical Chemistry Volume 3 https://doi.org/10.1524/9783486711639.293	book	January 2010
Multireference linearized coupled cluster theory for strongly correlated systems using matrix product states. Sharma, Sandeep; Alavi, Ali Apollo - University of Cambridge Repository https://doi.org/10.17863/cam.32445	text	January 2015
Analytic response theory for the density matrix renormalization group Dorando, Jonathan J.; Hachmann, Johannes; Chan, Garnet Kin-Lic arXiv https://doi.org/10.48550/arxiv.0901.3166	text	January 2009
Optimizing Hartree-Fock orbitals by the density-matrix renormalization group Luo, H. -G.; Qin, M. -P.; Xiang, T. arXiv https://doi.org/10.48550/arxiv.1002.1287	text	January 2010
The density-matrix renormalization group in the age of matrix product states Schollwoeck, Ulrich arXiv https://doi.org/10.48550/arxiv.1008.3477	text	January 2010
Longitudinal static optical properties of hydrogen chains: finite field extrapolations of matrix product state calculations Wouters, Sebastian; Limacher, Peter A.; Van Neck, Dimitri arXiv https://doi.org/10.48550/arxiv.1202.0177	text	January 2012
CheMPS2: a free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry Wouters, Sebastian; Poelmans, Ward; Ayers, Paul W. arXiv https://doi.org/10.48550/arxiv.1312.2415	text	January 2013
Determining Factors for the Accuracy of DMRG in Chemistry Keller, Sebastian F.; Reiher, Markus arXiv https://doi.org/10.48550/arxiv.1401.5497	text	January 2014
Investigation of metal-insulator like transition through the ab initio density matrix renormalization group approach Fertitta, E.; Paulus, B.; Barcza, G. arXiv https://doi.org/10.48550/arxiv.1406.7038	text	January 2014
Matrix Product State applications for the ALPS project Dolfi, Michele; Bauer, Bela; Keller, Sebastian arXiv https://doi.org/10.48550/arxiv.1407.0872	text	January 2014
The density matrix renormalization group for ab initio quantum chemistry Wouters, Sebastian; Van Neck, Dimitri arXiv https://doi.org/10.48550/arxiv.1407.2040	text	January 2014
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Two-Dimensional Tensor Product Variational Formulation Nishino, Tomotoshi; Hieida, Yasuhiro; Okunishi, Kouichi arXiv https://doi.org/10.48550/arxiv.cond-mat/0011103	text	January 2000
Parallelization Strategies for Density Matrix Renormalization Group Algorithms on Shared-Memory Systems Hager, G.; Jeckelmann, E.; Fehske, H. arXiv https://doi.org/10.48550/arxiv.cond-mat/0305463	text	January 2003
Quantum data compression, quantum information generation, and the density-matrix renormalization group method Legeza, Ö.; Sólyom, J. arXiv https://doi.org/10.48550/arxiv.cond-mat/0401136	text	January 2004
Real time evolution using the density matrix renormalization group White, Steven R.; Feiguin, Adrian E. arXiv https://doi.org/10.48550/arxiv.cond-mat/0403310	text	January 2004
Multireference Correlation in Long Molecules with the Quadratic Scaling Density Matrix Renormalization Group Hachmann, Johannes; Cardoen, Wim; Chan, Garnet Kin-Lic arXiv https://doi.org/10.48550/arxiv.cond-mat/0606115	text	January 2006
From density-matrix renormalization group to matrix product states McCulloch, Ian P. arXiv https://doi.org/10.48550/arxiv.cond-mat/0701428	text	January 2007
Density-matrix renormalization-group method in momentum space Xiang, T. arXiv https://doi.org/10.48550/arxiv.cond-mat/9603020	text	January 1996
Efficient simulation of one-dimensional quantum many-body systems Vidal, G. arXiv https://doi.org/10.48550/arxiv.quant-ph/0310089	text	January 2003

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Automated Identification of Relevant Frontier Orbitals for Chemical Compounds and Processes Stein, Christopher J.; Reiher, Markus arXiv https://doi.org/10.48550/arxiv.1702.00450	text	January 2017
Efficient reconstruction of CASCI-type wave functions for a DMRG state using quantum information theory and genetic algorithm Luo, Zhen; Ma, Yingjin; Liu, Chungen arXiv https://doi.org/10.48550/arxiv.1704.08817	text	January 2017
A Perturbative Density Matrix Renormalization Group Algorithm for Large Active Spaces Guo, Sheng; Li, Zhendong; Chan, Garnet Kin-Lic arXiv https://doi.org/10.48550/arxiv.1803.07150	preprint	January 2018
Low-rank representation of tensor network operators with long-range pairwise interactions Lin, Lin; Tong, Yu arXiv https://doi.org/10.48550/arxiv.1909.02206	preprint	January 2019
Massively parallel quantum chemical density matrix renormalization group method Brabec, Jiří; Brandejs, Jan; Kowalski, Karol arXiv https://doi.org/10.48550/arxiv.2001.04890	preprint	January 2020
A General Automatic Method for Optimal Construction of Matrix Product Operators Using Bipartite Graph Theory Ren, Jiajun; Li, Weitang; Jiang, Tong arXiv https://doi.org/10.48550/arxiv.2006.02056	text	January 2020
Quantum Tensor Networks, Stochastic Processes, and Weighted Automata Srinivasan, Siddarth; Adhikary, Sandesh; Miller, Jacob arXiv https://doi.org/10.48550/arxiv.2010.10653	preprint	January 2020

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37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
71 CLASSICAL AND QUANTUM MECHANICS
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