References
Citing MPSKit
If you use MPSKit in your research, please cite it: ( DocumenterCitations.CitationSiteNode("devos2026mpskit-cite-1")
). The CITATION.cff file in the repository carries the up-to-date metadata, including the DOI of the specific release you used.
Please consider citing TensorKit.jl as well: ( DocumenterCitations.CitationSiteNode("devos2025tensorkit-cite-1")
). It provides the (symmetric) tensors that MPSKit is built on, and does much of the heavy lifting behind every algorithm here.
Publications using MPSKit
Below you can find a list of publications that have made use of MPSKit. If you have used this package and wish to have your publication added to this list, please open a pull request or an issue on the GitHub repository.
2026
Basumatary, U.; Sinha, A. and Zhou, X. (Mar 2026). Cosmological Correlators Using Tensor Networks, arXiv:2603.26090 [hep-th].
Brehmer, P.; Burgelman, L.; Yue, Z.-Y.; Fedorovich, G.; Haegeman, J. and Devos, L. (May 2026). PEPSKit.jl: A Julia Package for Projected Entangled-Pair State Simulations, arXiv:2605.19960 [cond-mat.str-el].
Burgelman, L.; Francuz, A.; Brehmer, P.; Devos, L.; Haegeman, J.; Verstraete, F. and Vanhecke, B. (2026). Implicit differentiation of tensor network algorithms, arXiv:2607.15030 [quant-ph].
Hörmann, M. (Jun 2026). Folds of One Curve: The Superradiant Phase Diagram of Dicke Modes with Interacting Matter, arXiv:2606.26081 [cond-mat.str-el].
Kadow, W.; Morera, I.; Demler, E. and Knap, M. (Mar 2026). Fractionalization from Kinetic Frustration in Doped Two-Dimensional SU(4) Quantum Magnets, arXiv:2603.28871 [cond-mat.str-el].
Kaplan, M. and Tilloy, A. (Jun 2026). Wavelet Matrix Product States for Quantum Fields, arXiv:2606.23823 [quant-ph].
Lu, D.-C.; Chatterjee, A. and Tantivasadakarn, N. (Feb 2026). Generalized Kramers-Wannier Self-Duality in Hopf-Ising Models, arXiv:2602.10183 [cond-mat.str-el].
Ritter, M. K. (Apr 2026). Fast Elementwise Operations on Tensor Trains with Alternating Cross Interpolation, arXiv:2604.00037 [math.NA].
Shankar, A.; Van Acoleyen, K. and Haegeman, J. (Jun 2026). Finite-Element Matrix Product States for Continuum Models in One Dimension, arXiv:2606.14873 [quant-ph].
Staelens, Q.; Verraes, D.; Vrancken, D.; Braeckevelt, T.; Haegeman, J. and Van Speybroeck, V. (Feb 2026). Combining Matrix Product States and Mean-Field Theory to Capture Magnetic Order in Quasi-1D Cuprates, arXiv:2602.21695 [cond-mat.str-el].
Ueda, A.; Numasawa, T.; De Vos, B. and Watanabe, M. (Jun 2026). Emergent Andreev Reflection from a Lattice Duality Defect, arXiv:2606.23684 [cond-mat.str-el].
Vanthilt, V.; Van Damme, M.; Haegeman, J.; McCulloch, I. P. and Vanderstraeten, L. (May 2026). Matrix Product Operator Encodings of the Magnus Expansion and Dyson Series, arXiv:2605.21597 [quant-ph].
Veitas, R.; Khalifa, A.; Machado, F. and Chatterjee, S. (May 2026). Fluctuation-Driven Chiral Ferromagnetism, arXiv:2605.06852 [cond-mat.str-el].
Yang, Q. (Jun 2026). Transfer-Matrix Functions for Algebraically Decaying Interactions in Variational Infinite Matrix Product States, arXiv:2606.20522 [cond-mat.str-el].
Zemlevskiy, N. A. (Mar 2026). Exclusive Scattering Channels from Entanglement Structure in Real-Time Simulations, arXiv:2603.15621 [quant-ph].
Zong, Y.-Y.; Gu, Z.-L. and Li, J.-X. (2026). Pseudogap with Fermi Arcs and Fermi Pockets in Half-Filled Twisted Transition Metal Dichalcogenides. Physical Review X 16, 011005, arXiv:2406.11374.
Zong, Y.-Y.; Yu, S.-L. and Li, J.-X. (May 2026). Correlation-Driven Orbital-Selective Fermiology and Superconductivity in the Bilayer Nickelate La
Ni O , arXiv:2605.10101 [cond-mat.str-el]. Vancraeynest-De Cuiper, B.; Wiesiolek, W. and Verstraete, F. (2026). Les Houches Lecture Notes on Tensor Networks. SciPost Physics Lecture Notes, 128, arXiv:2512.24390.
2025
Capponi, S.; Devos, L.; Lecheminant, P.; Totsuka, K. and Vanderstraeten, L. (2025). Non-Landau Quantum Phase Transition in Modulated SU(
) Heisenberg Spin Chains. Physical Review B 111, L020404. Dempsey, R.; Glück, A.-M. E.; Pufu, S. S. and Søgaard, B. T. (Aug 2025). Infinite Matrix Product States for
Herviou, L.; Rey, A. and Mila, F. (2025). Singularity with and without Disorder at Affleck-Kennedy-Lieb-Tasaki Points. Physical Review B 111, L161118.
Kirchner, N.; Moessner, R.; Pollmann, F. and Gammon-Smith, A. (Jul 2025). Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling, arXiv:2507.22115 [cond-mat].
Linden, V. V.; Vos, B. D.; Vervoort, K.; Verstraete, F. and Ueda, A. (Jul 2025). Spiral Renormalization Group Flow and Universal Entanglement Spectrum of the Non-Hermitian 5-State Potts Model, arXiv:2507.14732 [cond-mat].
Maertens, D.; Haegeman, J. and Acoleyen, K. V. (Aug 2025). Real-Time Bubble Nucleation and Growth for False Vacuum Decay on the Lattice, arXiv:2508.13645 [cond-mat].
Mortier, Q.; Devos, L.; Burgelman, L.; Vanhecke, B.; Bultinck, N.; Verstraete, F.; Haegeman, J. and Vanderstraeten, L. (2025). Fermionic Tensor Network Methods. SciPost Physics 18, 012.
Shen, C. (Feb 2025). _Exploring the Phase Diagram of SU(2)4 Strange Correlator, arXiv:2502.14556 [hep-th].
Sinha, A. and Basumatary, U. (Dec 2025). Lectures on Quantum Field Theory on a Quantum Computer, arXiv:2512.02706 [quant-ph].
Sommer, O. E.; Wen, X. and Vishwanath, A. (2025). Higher Berry Curvature from the Wave Function. I. Schmidt Decomposition and Matrix Product States. Physical Review Letters 134, 146601, arXiv:2405.05316.
Ueda, A.; Inamura, K. and Ohmori, K. (2025). Chiral Edge States Emerging on Anyon-Net. SciPost Physics Core 8, 062.
Vrancken, D.; Ganne, S.; Verraes, D.; Braeckevelt, T.; Devos, L.; Vanderstraeten, L.; Haegeman, J. and Van Speybroeck, V. (2025). Quantitative Description of Strongly Correlated Materials by Combining Downfolding Techniques and Tensor Networks. Journal of Chemical Theory and Computation 21, 7830–7844.
Van Damme, M.; Mildenberger, J.; Grusdt, F.; Hauke, P. and Halimeh, J. C. (2025). Suppressing Nonperturbative Gauge Errors in the Thermodynamic Limit Using Local Pseudogenerators. Communications Physics 8, 106, arXiv:2110.08041.
2024
Belyansky, R.; Whitsitt, S.; Mueller, N.; Fahimniya, A.; Bennewitz, E. R.; Davoudi, Z. and Gorshkov, A. V. (2024). High-Energy Collision of Quarks and Mesons in the Schwinger Model: From Tensor Networks to Circuit QED. Physical Review Letters 132, 091903.
Crotti, S.; Barthel, T. and Braunstein, A. (2024). Nonequilibrium Steady-State Dynamics of Markov Processes on Graphs, arXiv.2411.19100, arXiv:2411.19100 [cond-mat].
Rogerson, D. and Roy, A. (2024). Quantum Circuit Optimization Using Differentiable Programming of Tensor Network States, arXiv:2408.12583, arXiv:2408.12583 [quant-ph].
Ueda, A.; Inamura, K. and Ohmori, K. (2024). Chiral Edge States Emerging on Anyon-Net, arXiv:2408.02724, arXiv:2408.02724 [cond-mat].
Weerda, E. L. and Rizzi, M. (2024). Fractional Quantum Hall States with Variational Projected Entangled-Pair States: A Study of the Bosonic Harper-Hofstadter Model. Physical Review B 109, L241117.
2023
- Zhang, Y.; Hulsch, A.; Zhang, H.-C.; Tang, W.; Wang, L. and Tu, H.-H. (2023). Universal Scaling of Klein Bottle Entropy near Conformal Critical Points. Physical Review Letters 130, 151602.
2022
Devos, L.; Vanderstraeten, L. and Verstraete, F. (2022). Haldane Gap in the SU(3) [3 0 0] Heisenberg Chain. Physical Review B 106, 155103.
Halimeh, J. C.; Damme, M. V.; Zache, T. V.; Banerjee, D. and Hauke, P. (2022). Achieving the Quantum Field Theory Limit in Far-from-Equilibrium Quantum Link Models. Quantum 6, 878.
Roose, G.; Haegeman, J.; Van Acoleyen, K.; Vanderstraeten, L. and Bultinck, N. (2022). The Chiral Gross-Neveu Model on the Lattice via a Landau-forbidden Phase Transition. Journal of High Energy Physics 2022, 19.
Van Damme, M.; Zache, T. V.; Banerjee, D.; Hauke, P. and Halimeh, J. C. (2022). Dynamical Quantum Phase Transitions in Spin-
Quantum Link Models. Physical Review B 106, 245110. Vanhove, R.; Lootens, L.; Van Damme, M.; Wolf, R.; Osborne, T. J.; Haegeman, J. and Verstraete, F. (2022). Critical Lattice Model for a Haagerup Conformal Field Theory. Physical Review Letters 128, 231602.
2021
Halimeh, J. C.; Trapin, D.; Van Damme, M. and Heyl, M. (2021). Local Measures of Dynamical Quantum Phase Transitions. Physical Review B 104, 075130.
Hauru, M.; Van Damme, M. and Haegeman, J. (2021). Riemannian Optimization of Isometric Tensor Networks. SciPost Physics 10, 040.
Roose, G.; Bultinck, N.; Vanderstraeten, L.; Verstraete, F.; Van Acoleyen, K. and Haegeman, J. (2021). Lattice Regularisation and Entanglement Structure of the Gross-Neveu Model. Journal of High Energy Physics 2021, 207.
Van Damme, M.; Vanhove, R.; Haegeman, J.; Verstraete, F. and Vanderstraeten, L. (2021). Efficient Matrix Product State Methods for Extracting Spectral Information on Rings and Cylinders. Physical Review B 104, 115142.
Yu, C. and Lee, J.-W. (2021). Closing of the Haldane Gap in a Spin-1 XXZ Chain. Journal of the Korean Physical Society 79, 841–845.
2019
- Roose, G.; Vanderstraeten, L.; Haegeman, J. and Bultinck, N. (2019). Anomalous Domain Wall Condensation in a Modified Ising Chain. Physical Review B 99, 195132.
Full list of references
Ceruti, G. and Lubich, C. (2022). An Unconventional Robust Integrator for Dynamical Low-Rank Approximation. BIT Numerical Mathematics 62, 23–44.
Chepiga, N. and Mila, F. (2017). Excitation Spectrum and Density Matrix Renormalization Group Iterations. Physical Review B 96, 054425.
Devos, L. and Haegeman, J. (Aug 2025). TensorKit.jl: A Julia Package for Large-Scale Tensor Computations, with a Hint of Category Theory, arXiv:2508.10076 [cs.MS].
Devos, L.; Van Damme, M. and Haegeman, J. (Jun 2026). MPSKit.jl.
Gleis, A.; Li, J.-W. and von Delft, J. (2023). Controlled Bond Expansion for Density Matrix Renormalization Group Ground State Search at Single-Site Costs. Physical Review Letters 130, 246402.
Haegeman, J.; Cirac, J. I.; Osborne, T. J.; Pižorn, I.; Verschelde, H. and Verstraete, F. (2011). Time-Dependent Variational Principle for Quantum Lattices. Physical Review Letters 107, 070601.
Haegeman, J.; Michalakis, S.; Nachtergaele, B.; Osborne, T. J.; Schuch, N. and Verstraete, F. (2013). Elementary Excitations in Gapped Quantum Spin Systems. Physical Review Letters 111, 080401.
Hubig, C.; McCulloch, I. P.; Schollwöck, U. and Wolf, F. A. (2015). Strictly single-site DMRG algorithm with subspace expansion. Phys. Rev. B 91, 155115.
Jeckelmann, E. (2002). Dynamical Density-Matrix Renormalization-Group Method. Physical Review B 66, 045114.
Paeckel, S.; Köhler, T.; Swoboda, A.; Manmana, S. R.; Schollwöck, U. and Hubig, C. (2019). Time-Evolution Methods for Matrix-Product States. Annals of Physics 411, 167998.
Parker, D. E.; Cao, X. and Zaletel, M. P. (2020). Local Matrix Product Operators: Canonical Form, Compression, and Control Theory. Physical Review B 102, 035147.
Pollmann, F.; Mukerjee, S.; Turner, A. M. and Moore, J. E. (2009). Theory of Finite-Entanglement Scaling at One-Dimensional Quantum Critical Points. Physical Review Letters 102, 255701.
Stoudenmire, E. M. and White, S. R. (2010). Minimally Entangled Typical Thermal State Algorithms. New Journal of Physics 12, 055026, arXiv:1002.1305 [cond-mat.str-el].
Van Damme, M.; Haegeman, J.; McCulloch, I. and Vanderstraeten, L. (2024). Efficient Higher-Order Matrix Product Operators for Time Evolution. SciPost Physics 17, 135.
Vanderstraeten, L.; Haegeman, J. and Verstraete, F. (2019). Tangent-Space Methods for Uniform Matrix Product States. SciPost Physics Lecture Notes, 7.
Vanhecke, B.; Van Damme, M.; Haegeman, J.; Vanderstraeten, L. and Verstraete, F. (2021). Tangent-Space Methods for Truncating Uniform MPS. SciPost Physics Core 4, 004.
Zaletel, M. P.; Mong, R. S.; Karrasch, C.; Moore, J. E. and Pollmann, F. (2015). Time-Evolving a Matrix Product State with Long-Ranged Interactions. Physical Review B 91, 165112.
Zauner-Stauber, V.; Vanderstraeten, L.; Fishman, M. T.; Verstraete, F. and Haegeman, J. (2018). Variational Optimization Algorithms for Uniform Matrix Product States. Physical Review B 97, 045145.