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Efficient numerical simulations with Tensor Networks: Tensor Network Python (TeNPy)
Open accessAbstract
Tensor product state (TPS) based methods are powerful tools to efficiently simulate quantum many-body systems in and out of equilibrium. In particular, the one-dimensional matrix-product (MPS) formalism is by now an established tool in condensed matter theory and quantum chemistry. In these lecture notes, we combine a compact review of basic TPS concepts with the introduction of a versatile tensor library for Python (TeNPy) [1]. As concrete examples, we consider the MPS based time-evolving block decimation and the density matrix renormalization group algorithm. Moreover, we provide a practical guide on how to implement abelian symmetries (e.g., a particle number conservation) to accelerate tensor operations.
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Citations
Cites
Possible highT c superconductivity in the Ba?La?Cu?O system
Bednorz, J. G., & M�ller, K. A. (1986) · Zeitschrift f�r Physik B Condensed Matter · doi:10.1007/bf01303701 · Cited by 14,319
Density matrix formulation for quantum renormalization groups
White, S. R. (1992) · Physical Review Letters · doi:10.1103/physrevlett.69.2863 · Cited by 7,702
Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
Laughlin, R. B. (1983) · Physical Review Letters · doi:10.1103/physrevlett.50.1395 · Cited by 5,749
The density-matrix renormalization group in the age of matrix product states
Schollwöck, U. (2011) · Annals of Physics · doi:10.1016/j.aop.2010.09.012 · Cited by 4,818
Two-Dimensional Magnetotransport in the Extreme Quantum Limit
Tsui, D. C., Stormer, H. L., & Gossard, A. C. (1982) · Physical Review Letters · doi:10.1103/physrevlett.48.1559 · Cited by 4,788
Haldane, F. D. M. (1983) · Physical Review Letters · doi:10.1103/physrevlett.50.1153 · Cited by 3,695
Python for scientific computing
Oliphant, T. E. (2007) · Computing in Science & Engineering · doi:10.1109/mcse.2007.58 · Cited by 3,303 · cited 1×
“np_conserved, which also contains functions for all the basic operations on tensors represented by an Array class, with an interface very similar to that of the NumPy (and SciPy) library [68].”
MethodEntanglement Entropy and Quantum Field Theory
Calabrese, P., & Cardy, J. (2004) · arXiv · doi:10.48550/arxiv.hep-th/0405152 · Cited by 3,275
Entanglement entropy and quantum field theory
Calabrese, P., & Cardy, J. (2004) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2004/06/p06002 · Cited by 3,275
Haldane, F. D. M. (1983) · Physics Letters A · doi:10.1016/0375-9601(83)90631-x · Cited by 2,883
Colloquium : Area laws for the entanglement entropy
Eisert, J., Cramer, M., & Plenio, M. B. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.277 · Cited by 2,873
Resonating valence bonds: A new kind of insulator?
Anderson, P. W. (1973) · Materials Research Bulletin · doi:10.1016/0025-5408(73)90167-0 · Cited by 2,823
Entanglement in Quantum Critical Phenomena
Vidal, G., Latorre, J. I., Rico, E., & Kitaev, A. (2003) · Physical Review Letters · doi:10.1103/physrevlett.90.227902 · Cited by 2,793
Topological Entanglement Entropy
Kitaev, A., & Preskill, J. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.110404 · Cited by 2,430
Orús, R. (2014) · Annals of Physics · doi:10.1016/j.aop.2014.06.013 · Cited by 2,255
Rigorous results on valence-bond ground states in antiferromagnets
Affleck, I., Kennedy, T., Lieb, E. H., & Tasaki, H. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.799 · Cited by 2,223
Detecting Topological Order in a Ground State Wave Function
Levin, M., & Wen, X.-G. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.110405 · Cited by 2,068
Efficient Simulation of One-Dimensional Quantum Many-Body Systems
Vidal, G. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.040502 · Cited by 1,779
Verstraete, F., Murg, V., & Cirac, J. I. (2008) · Advances in Physics · doi:10.1080/14789940801912366 · Cited by 1,762
Li, H., & Haldane, F. D. M. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.010504 · Cited by 1,652
Average entropy of a subsystem
Page, D. N. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.1291 · Cited by 1,578
Finitely correlated states on quantum spin chains
Fannes, M., Nachtergaele, B., & Werner, R. F. (1992) · Communications in Mathematical Physics · doi:10.1007/bf02099178 · Cited by 1,422
Real-Time Evolution Using the Density Matrix Renormalization Group
White, S. R., & Feiguin, A. E. (2004) · Physical Review Letters · doi:10.1103/physrevlett.93.076401 · Cited by 1,398
Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
Daley, A. J., Kollath, C., Schollwöck, U., & Vidal, G. (2004) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2004/04/p04005 · Cited by 1,160
An area law for one-dimensional quantum systems
Hastings, M. B. (2007) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2007/08/p08024 · Cited by 1,131
Thermodynamic limit of density matrix renormalization.
Östlund, S., & Rommer, S. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.3537 · Cited by 1,077
Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension
Vidal, G. (2007) · Physical Review Letters · doi:10.1103/physrevlett.98.070201 · Cited by 907
Time-Dependent Variational Principle for Quantum Lattices
Haegeman, J., Cirac, J. I., Osborne, T. J., Pižorn, I., Verschelde, H., & Verstraete, F. (2011) · Physical Review Letters · doi:10.1103/physrevlett.107.070601 · Cited by 865
The Density Matrix Renormalization Group in Quantum Chemistry
Chan, G. K.-L., & Sharma, S. (2011) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-032210-103338 · Cited by 822
Unifying time evolution and optimization with matrix product states
Haegeman, J., Lubich, C., Oseledets, I., Vandereycken, B., & Verstraete, F. (2016) · Physical Review B · doi:10.1103/physrevb.94.165116 · Cited by 804
Suzuki, M. (1991) · Journal of Mathematical Physics · doi:10.1063/1.529425 · Cited by 762
Classical Simulation of Infinite-Size Quantum Lattice Systems in Two Spatial Dimensions
Jordan, J., Orús, R., Vidal, G., Verstraete, F., & Cirac, J. I. (2008) · Physical Review Letters · doi:10.1103/physrevlett.101.250602 · Cited by 710
Tensor Renormalization Group Approach to Two-Dimensional Classical Lattice Models
Levin, M., & Nave, C. P. (2007) · Physical Review Letters · doi:10.1103/physrevlett.99.120601 · Cited by 606
Infinite time-evolving block decimation algorithm beyond unitary evolution
Orús, R., & Vidal, G. (2008) · Physical Review B · doi:10.1103/physrevb.78.155117 · Cited by 467
Corner Transfer Matrix Renormalization Group Method
Nishino, T., & Okunishi, K. (1996) · Journal of the Physical Society of Japan · doi:10.1143/jpsj.65.891 · Cited by 467
From density-matrix renormalization group to matrix product states
McCulloch, I. P. (2007) · Journal of Statistical Mechanics: Theory and Experiment · doi:10.1088/1742-5468/2007/10/p10014 · Cited by 460
Rommer, S., & Östlund, S. (1997) · Physical Review B · doi:10.1103/physrevb.55.2164 · Cited by 431
Entropy Scaling and Simulability by Matrix Product States
Schuch, N., Wolf, M. M., Verstraete, F., & Cirac, J. I. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.030504 · Cited by 409
Entanglement spectrum in one-dimensional systems
Calabrese, P., & Lefevre, A. (2008) · Physical Review A · doi:10.1103/physreva.78.032329 · Cited by 399
Theory of Finite-Entanglement Scaling at One-Dimensional Quantum Critical Points
Pollmann, F., Mukerjee, S., Turner, A. M., & Moore, J. E. (2009) · Physical Review Letters · doi:10.1103/physrevlett.102.255701 · Cited by 364
Self-citationTensor Network Renormalization
Evenbly, G., & Vidal, G. (2015) · Physical Review Letters · doi:10.1103/physrevlett.115.180405 · Cited by 362
Time-evolving a matrix product state with long-ranged interactions
Zaletel, M. P., Mong, R. S. K., Karrasch, C., Moore, J. E., & Pollmann, F. (2015) · Physical Review B · doi:10.1103/physrevb.91.165112 · Cited by 323
Self-citationScaling of entanglement support for matrix product states
Tagliacozzo, L., de Oliveira, T. R., Iblisdir, S., & Latorre, J. I. (2008) · Physical Review B · doi:10.1103/physrevb.78.024410 · Cited by 314
Minimally entangled typical thermal state algorithms
Stoudenmire, E. M., & White, S. R. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/5/055026 · Cited by 301
Tensor network states and algorithms in the presence of a global U(1) symmetry
Singh, S., Pfeifer, R. N. C., & Vidal, G. (2011) · Physical Review B · doi:10.1103/physrevb.83.115125 · Cited by 287
Tensor network decompositions in the presence of a global symmetry
Singh, S., Pfeifer, R. N. C., & Vidal, G. (2010) · Physical Review A · doi:10.1103/physreva.82.050301 · Cited by 279
Variational optimization algorithms for uniform matrix product states
Zauner-Stauber, V., Vanderstraeten, L., Fishman, M. T., Verstraete, F., & Haegeman, J. (2018) · Physical Review B · doi:10.1103/physrevb.97.045145 · Cited by 270
Non-abelian symmetries in tensor networks: A quantum symmetry space approach
Weichselbaum, A. (2012) · Annals of Physics · doi:10.1016/j.aop.2012.07.009 · Cited by 268
The non-Abelian density matrix renormalization group algorithm
McCulloch, I. P., & Gulácsi, M. (2002) · Europhysics Letters (EPL) · doi:10.1209/epl/i2002-00393-0 · Cited by 242
Density matrix renormalization group algorithms with a single center site
White, S. R. (2005) · Physical Review B · doi:10.1103/physrevb.72.180403 · Cited by 238
Finite automata for caching in matrix product algorithms
Crosswhite, G. M., & Bacon, D. (2008) · Physical Review A · doi:10.1103/physreva.78.012356 · Cited by 172
Strictly single-site DMRG algorithm with subspace expansion
Hubig, C., McCulloch, I. P., Schollwöck, U., & Wolf, F. A. (2015) · Physical Review B · doi:10.1103/physrevb.91.155115 · Cited by 171
Loop Optimization for Tensor Network Renormalization
Yang, S., Gu, Z.-C., & Wen, X.-G. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.110504 · Cited by 167
Khemani, V., Pollmann, F., & Sondhi, S. L. (2016) · Physical Review Letters · doi:10.1103/physrevlett.116.247204 · Cited by 163
Self-citationYu, X., Pekker, D., & Clark, B. K. (2017) · Physical Review Letters · doi:10.1103/physrevlett.118.017201 · Cited by 140
Tensor network states and algorithms in the presence of a global SU(2) symmetry
Singh, S., & Vidal, G. (2012) · Physical Review B · doi:10.1103/physrevb.86.195114 · Cited by 137
Liang, S., & Pang, H. (1994) · Physical review. B, Condensed matter · doi:10.1103/physrevb.49.9214 · Cited by 105
Real-space parallel density matrix renormalization group
Stoudenmire, E. M., & White, S. R. (2013) · Physical Review B · doi:10.1103/physrevb.87.155137 · Cited by 100
Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
Ehlers, G., White, S. R., & Noack, R. M. (2017) · Physical review. B./Physical review. B · doi:10.1103/physrevb.95.125125 · Cited by 95
Efficient variational diagonalization of fully many-body localized Hamiltonians
Pollmann, F., Khemani, V., Cirac, J. I., & Sondhi, S. L. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.94.041116 · Cited by 91
Self-citationDensity matrix renormalization group on a cylinder in mixed real and momentum space
Motruk, J., Zaletel, M. P., Mong, R. S. K., & Pollmann, F. (2016) · Physical review. B./Physical review. B · doi:10.1103/physrevb.93.155139 · Cited by 82
Self-citationGauge fixing, canonical forms, and optimal truncations in tensor networks with closed loops
Evenbly, G. (2018) · Physical review. B./Physical review. B · doi:10.1103/physrevb.98.085155 · Cited by 78
Entanglement versus gap for one-dimensional spin systems
Gottesman, D., & Hastings, M. B. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/2/025002 · Cited by 70
Error estimates for extrapolations with matrix-product states
Hubig, C., Haegeman, J., & Schollwöck, U. (2018) · Physical Review B · doi:10.1103/physrevb.97.045125 · Cited by 59
Hastings, M. B. (2009) · Journal of Mathematical Physics · doi:10.1063/1.3149556 · Cited by 50
Automated construction of $U(1)$-invariant matrix-product operators from graph representations
Paeckel, S., Köhler, T., & Manmana, S. R. (2017) · SciPost Physics · doi:10.21468/scipostphys.3.5.035 · Cited by 37
Numerical computation of dynamically important excited states of many-body systems
Łącki, M., Delande, D., & Zakrzewski, J. (2012) · Physical Review A · doi:10.1103/physreva.86.013602 · Cited by 13
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Fishman, M., White, S., & Stoudenmire, E. M. (2022) · SciPost Physics Codebases · doi:10.21468/scipostphyscodeb.4 · Cited by 1,084
Evidence for the utility of quantum computing before fault tolerance
Kim, Y., Eddins, A., Anand, S., Wei, K. X., van den Berg, E., Rosenblatt, S., Nayfeh, H., Wu, Y., Zaletel, M., Temme, K., et al. (2023) · Nature · doi:10.1038/s41586-023-06096-3 · Cited by 1,050
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Scholl, P., Schuler, M., Williams, H. J., Eberharter, A. A., Barredo, D., Schymik, K.-N., Lienhard, V., Henry, L.-P., Lang, T. C., Lahaye, T., et al. (2021) · Nature · doi:10.1038/s41586-021-03585-1 · Cited by 688
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Hirthe, S., Chalopin, T., Bourgund, D., Bojović, P., Bohrdt, A., Demler, E., Grusdt, F., Bloch, I., & Hilker, T. A. (2023) · Nature · doi:10.1038/s41586-022-05437-y · Cited by 91
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Metadata
- Authors
- Hauschild, J., & Pollmann, F.
- Venue
- SciPost Physics Lecture Notes
- Publisher
- Stichting SciPost
- Published
- 2018-10-08
- ISSN
- 2590-1990 (ISSN-L)
- OpenAlex
- W2798727936
- Cited by
- 438
- References
- 67
- FWCI
- 10.63
- Type
- journal article
- Language
- en
- Open access
- diamond
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