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.
Li, J.-W.; Gleis, A. and von Delft, J. (2024). Time-Dependent Variational Principle with Controlled Bond Expansion for Matrix Product States. Physical Review Letters 133, 026401.
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.
Schollwöck, U. (2011). The density-matrix renormalization group in the age of matrix product states. Annals of Physics 326, 96–192.
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.