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We present a compendium of numerical simulation techniques, based on tensor network methods, aiming to address problems of many-body quantum mechanics on a classical computer.
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Entanglement properties of the harmonic chain ,
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Application of the density matrix renormalization group in momentum space ,
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Real-Time Evolution Using the Density Matrix Renormalization Group ,
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Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces ,
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Matrix product density operators: Simulation of finite-temperature and dissipative systems ,
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Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm ,
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Entanglement entropy and quantum field theory ,
P. Calabrese and J. Cardy, · 2004
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PROPACK-software for large and sparse SVD calculations ,
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Entropy, entanglement, and area: Analytical results for harmonic lattice systems ,
M. B. Plenio, J. Eisert, J. Dreißig and M. Cramer, · 2005
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The density-matrix renormalization group ,
U. Schollwöck, · 2005
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The fermionic canonical commutation relations and the Jordan-Wigner transform ,
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The one-dimensional Hubbard model ,
F. H. Essler, H. Frahm, F. Göhmann, A. Klümper and V. E. Korepin, · 2005
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Domain decomposition methods: algorithms and theory , vol. 34,
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Density matrix renormalization group algorithms with a single center site ,
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Violation of the entropic area law for fermions ,
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Spectral gap and exponential decay of correlations ,
M. B. Hastings and T. Koma, · 2006
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A renormalisation-group algorithm for eigenvalue density functions of interacting quantum systems ,
T. J. Osborne, · 2006
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Criticality, the area law, and the computational power of projected entangled pair states ,
F. Verstraete, M. M. Wolf, D. Perez-Garcia and J. I. Cirac, · 2006
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Classical simulation of quantum many-body systems with a tree tensor network ,
Y.-Y. Shi, L.-M. Duan and G. Vidal, · 2006
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Matrix product state representations ,
D. Pérez García, F. Verstraete, M. M. Wolf and J. I. Cirac, · 2007
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Classical simulation of infinite-size quantum lattice systems in one spatial dimension ,
G. Vidal, · 2007
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Computational complexity of projected entangled pair states ,
N. Schuch, M. M. Wolf, F. Verstraete and J. I. Cirac, · 2007
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A variational method based on weighted graph states ,
S. Anders, H. J. Briegel and W. Dür, · 2007
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Entanglement renormalization ,
G. Vidal, · 2007
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Classical simulation versus universality in measurement-based quantum computation ,
M. Van den Nest, W. Dür, G. Vidal and H. J. Briegel, · 2007
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Variational quantum Monte Carlo simulations with tensor-network states ,
A. W. Sandvik and G. Vidal, · 2007
Cited alongside, same era.
Matrix product states algorithms and continuous systems ,
S. Iblisdir, R. Orús and J. I. Latorre, · 2007
Cited alongside, same era.
Quench Dynamics and Nonequilibrium Phase Diagram of the Bose–Hubbard Model ,
C. Kollath, A. M. Läuchli and E. Altman, · 2007
Cited alongside, same era.
From density-matrix renormalization group to matrix product states ,
I. P. McCulloch, · 2007
Cited alongside, same era.
Monte Carlo Methods ,
M. H. Kalos and P. A. Whitlock, · 2008
Cited alongside, same era.
Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems ,
F. Verstraete, V. Murg and J. I. Cirac, · 2008
Matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions ,
B. Pirvu, J. Haegeman and F. Verstraete, · 2012
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Matrix product states for critical spin chains: Finite-size versus finite-entanglement scaling ,
B. Pirvu, G. Vidal, F. Verstraete and L. Tagliacozzo, · 2012
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Optimized decimation of tensor networks with super-orthogonalization for two-dimensional quantum lattice models ,
S.-J. Ran, W. Li, B. Xi, Z. Zhang and G. Su, · 2012
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The quantum mechanics of many-body systems ,
D. J. Thouless, · 2013
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Entanglement and tensor network states ,
J. Eisert, · 2013
Later among the works it cites.
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Cited alongside, same era.
Infinite size density matrix renormalization group, revisited ,
I. P. McCulloch, · 2008
Cited alongside, same era.
Infinite time-evolving block decimation algorithm beyond unitary evolution ,
R. Orús and G. Vidal, · 2008
Cited alongside, same era.
Applying matrix product operators to model systems with long-range interactions ,
G. M. Crosswhite, A. C. Doherty and G. Vidal, · 2008
Cited alongside, same era.
Class of quantum many-body states that can be efficiently simulated ,
G. Vidal, · 2008
Cited alongside, same era.
Simulation of time evolution with multiscale entanglement renormalization ansatz ,
M. Rizzi, S. Montangero and G. Vidal, · 2008
Cited alongside, same era.
Simulating quantum computation by contracting tensor networks ,
I. L. Markov and Y. Shi, · 2008
Cited alongside, same era.
Area laws in a many-body localized state and its implications for topological order ,
B. Bauer and C. Nayak, · 2013
Later among the works it cites.
Elementary excitations in gapped quantum spin systems ,
J. Haegeman, S. Michalakis, B. Nachtergaele, T. J. Osborne, N. Schuch and F. Verstraete, · 2013
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Branching MERA codes: a natural extension of polar codes ,
A. J. Ferris and D. Poulin, · 2013
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Atomic quantum simulation of U(N) and SU(N) non-abelian lattice gauge theories ,
D. Banerjee, M. Boegli, M. Dalmonte, E. Rico, P. Stebler, U.-J. Wiese and P. Zoller, · 2013
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The mass spectrum of the Schwinger model with matrix product states ,
M. C. Bañuls, K. Cichy, J. I. Cirac and K. Jansen, · 2013
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Full characterization of the quantum linear-zigzag transition in atomic chains ,
P. Silvi, G. De Chiara, T. Calarco, G. Morigi and S. Montangero, · 2013
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Calculus of continuous matrix product states ,
J. Haegeman, J. I. Cirac, T. J. Osborne and F. Verstraete, · 2013
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Heisenberg antiferromagnet on Cayley trees: Low-energy spectrum and even/odd site imbalance ,
H. J. Changlani, S. Ghosh, C. L. Henley and A. M. Läuchli, · 2013
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Reducing the numerical effort of finite-temperature density matrix renormalization group calculations ,
C. Karrasch, J. H. Bardarson and J. E. Moore, · 2013
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Topological Insulators and Topological Superconductors ,
B. A. Bernevig and T. L. Hughes, · 2013
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Improved numerical methods for infinite spin chains with long-range interactions ,
V. Nebendahl and W. Dür, · 2013
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Global symmetries in tensor network states: Symmetric tensors versus minimal bond dimension ,
S. Singh and G. Vidal, · 2013
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Efficient tree tensor network states (TTNS) for quantum chemistry: Generalizations of the density matrix renormalization group algorithm ,
N. Nakatani and G. K.-L. Chan, · 2013
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Area law and real-space renormalization ,
A. J. Ferris, · 2013
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Entanglement negativity in the critical ising chain ,
P. Calabrese, L. Tagliacozzo and E. Tonni, · 2013
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Theory of network contractor dynamics for exploring thermodynamic properties of two-dimensional quantum lattice models ,
S.-J. Ran, B. Xi, T. Liu and G. Su, · 2013
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Spread of correlations in long-range interacting quantum systems ,
P. Hauke and L. Tagliacozzo, · 2013
Later among the works it cites.
Quantum signatures of chaos , vol. 54,
F. Haake, · 2013
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A practical introduction to tensor networks: Matrix product states and projected entangled pair states ,
R. Orús, · 2014
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Advances on tensor network theory: symmetries, fermions, entanglement, and holography ,
R. Orús, · 2014
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Class of highly entangled many-body states that can be efficiently simulated ,
G. Evenbly and G. Vidal, · 2014
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Tensor networks and quantum error correction ,
A. J. Ferris and D. Poulin, · 2014
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Fourier transform for fermionic systems and the spectral tensor network ,
A. J. Ferris, · 2014
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Matrix product states for lattice field theories ,
M. C. Bañuls, K. Cichy, J. I. Cirac, K. Jansen and H. Saito, · 2014
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Tensor networks for lattice gauge theories with continuous groups ,
L. Tagliacozzo, A. Celi and M. Lewenstein, · 2014
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Ab initio characterization of the quantum linear-zigzag transition using density matrix renormalization group calculations ,
P. Silvi, T. Calarco, G. Morigi and S. Montangero, · 2014
Later among the works it cites.
Quantum trajectories and open many-body quantum systems ,
A. J. Daley, · 2014
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Characterizing the Haldane phase in quasi-one-dimensional spin-1 Heisenberg antiferromagnets ,
K. Wierschem and P. Sengupta, · 2014
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Topological transitions from multipartite entanglement with tensor networks: A procedure for sharper and faster characterization ,
R. Orús, T.-C. Wei, O. Buerschaper and A. García-Saez, · 2014
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Faster identification of optimal contraction sequences for tensor networks ,
R. N. Pfeifer, J. Haegeman and F. Verstraete, · 2014
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NCON: A tensor network contractor for MATLAB ,
R. N. Pfeifer, G. Evenbly, S. Singh and G. Vidal, · 2014
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Lattice gauge tensor networks ,
P. Silvi, E. Rico, T. Calarco and S. Montangero, · 2014
Later among the works it cites.
Unconstrained tree tensor network: An adaptive gauge picture for enhanced performance ,
M. Gerster, P. Silvi, M. Rizzi, R. Fazio, T. Calarco and S. Montangero, · 2014
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Optimal persistent currents for interacting bosons on a ring with a gauge field ,
M. Cominotti, D. Rossini, M. Rizzi, F. Hekking and A. Minguzzi, · 2014
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Mutual information area laws for thermal free fermions ,
H. Bernigau, M. J. Kastoryano and J. Eisert, · 2015
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Unbiased Monte Carlo for the age of tensor networks ,
A. J. Ferris, · 2015
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Variational Monte Carlo simulations using tensor-product projected states ,
O. Sikora, H.-W. Chang, C.-P. Chou, F. Pollmann and Y.-J. Kao, · 2015
Later among the works it cites.
Entanglement structure of the Hubbard model in momentum space ,
G. Ehlers, J. Sólyom, O. Legeza and R. M. Noack, · 2015
Later among the works it cites.
Non-Abelian string breaking phenomena with matrix product states ,
S. Kühn, E. Zohar, J. I. Cirac and M. C. Bañuls, · 2015
Later among the works it cites.
Time-evolving a matrix product state with long-ranged interactions ,
M. P. Zaletel, R. S. K. Mong, C. Karrasch, J. E. Moore and F. Pollmann, · 2015
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Strictly single-site DMRG algorithm with subspace expansion ,
C. Hubig, I. P. McCulloch, U. Schollwöck and F. A. Wolf, · 2015
Later among the works it cites.
A randomized blocked algorithm for efficiently computing rank-revealing factorizations of matrices ,
P.-G. Martinsson and S. Voronin, · 2015
Later among the works it cites.
Improved scaling of time-evolving block-decimation algorithm through reduced-rank randomized singular value decomposition ,
D. Tamascelli, R. Rosenbach and M. Plenio, · 2015
Later among the works it cites.
Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing ,
H. N. Phien, J. A. Bengua, H. D. Tuan, P. Corboz and R. Orús, · 2015
Later among the works it cites.
Lattice gauge theory simulations in the quantum information era ,
M. Dalmonte and S. Montangero, · 2016
Later among the works it cites.
Real-time dynamics in U(1) lattice gauge theories with tensor networks ,
T. Pichler, M. Dalmonte, E. Rico, P. Zoller and S. Montangero, · 2016
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Crossover from classical to quantum Kibble-Zurek scaling ,
P. Silvi, G. Morigi, T. Calarco and S. Montangero, · 2016
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Optimal control of complex atomic quantum systems ,
S. Van Frank, M. Bonneau, J. Schmiedmayer, S. Hild, C. Gross, M. Cheneau, I. Bloch, T. Pichler, A. Negretti, T. Calarco et al. , · 2016
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Positive tensor network approach for simulating open quantum many-body systems ,
A. H. Werner, D. Jaschke, P. Silvi, M. Kliesch, T. Calarco, J. Eisert and S. Montangero, · 2016
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Superfluid density and quasi-long-range order in the one-dimensional disordered Bose–Hubbard model ,
M. Gerster, M. Rizzi, F. Tschirsich, P. Silvi, R. Fazio and S. Montangero, · 2016
Later among the works it cites.
Unifying time evolution and optimization with matrix product states ,
J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken and F. Verstraete, · 2016
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Simulating open quantum dynamics with time-dependent variational matrix product states: Towards microscopic correlation of environment dynamics and reduced system evolution ,
F. A. Y. N. Schröder and A. W. Chin, · 2016
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Review of tensor network contraction approaches ,
S.-J. Ran, E. Tirrito, C. Peng, X. Chen, G. Su and M. Lewenstein, · 2017
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Density of states of many-body quantum systems from tensor networks ,
F. Schrodi, P. Silvi, F. Tschirsich, R. Fazio and S. Montangero, · 2017
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Few-body systems capture many-body physics: Tensor network approach ,
S.-J. Ran, A. Piga, C. Peng, G. Su and M. Lewenstein, · 2017
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Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model ,
G. Ehlers, S. R. White and R. M. Noack, · 2017
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Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks ,
B. Buyens, S. Montangero, J. Haegeman, F. Verstraete and K. V. Acoleyen, · 2017
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Dynamics of the quantum phase transition in the one-dimensional Bose–Hubbard model: Excitations and correlations induced by a quench ,
B. Gardas, J. Dziarmaga and W. H. Zurek, · 2017
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OpenBLAS ,
Z. Xianyi, W. Qian and W. Saar, · 2017
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The tensor network theory library ,
S. Al-Assam, S. R. Clark and D. Jaksch, · 2017
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arpack-ng ,
D. Sorensen, R. Lehoucq, C. Yang, K. Maschhoff, S. Ledru and A. Cornet, · 2017
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LAPACK ,
Netlib, · 2017
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Fractional quantum Hall effect in the interacting Hofstadter model via tensor networks ,
M. Gerster, M. Rizzi, P. Silvi, M. Dalmonte and S. Montangero, · 2017
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URL https://uni10.gitlab.io/ (2018)
Universal Tensor Network Library – Uni10 version 2.0.0 , · 2018
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Probabilistic low-rank factorization accelerates tensor network simulations of critical quantum many-body ground states ,
L. Kohn, F. Tschirsich, M. Keck, M. B. Plenio, D. Tamascelli and S. Montangero, · 2018
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A programming guide for tensor networks with global SU(2) symmetry ,
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