Update list of works that use MPSKit (#344)

* add some references

* add reference links

* add some more references

* more references

* fix formatting

* Add GitHub Actions workflow for PR documentation comment

Author: lkdvos

.github/workflows/PR_comment.yml

@@ -0,0 +1,17 @@
+name: Docs preview comment
+on:
+  pull_request:
+    types: [labeled]
+
+permissions:
+  pull-requests: write
+jobs:
+  pr_comment:
+    runs-on: ubuntu-latest
+    steps:
+      - name: Create PR comment
+        if: github.event_name == 'pull_request' && github.repository == github.event.pull_request.head.repo.full_name && github.event.label.name == 'documentation'
+        uses: thollander/actions-comment-pull-request@v3
+        with:
+          message: 'After the build completes, the updated documentation will be available [here](https://quantumkithub.github.io/MPSKit.jl/previews/PR${{ github.event.number }}/)'
+          comment-tag: 'preview-doc'

docs/src/assets/mpskit.bib

@@ -59,6 +59,23 @@ @article{crotti2024
   keywords = {Condensed Matter - Disordered Systems and Neural Networks,Condensed Matter - Statistical Mechanics}
 }
 
+@misc{dempsey2025,
+  title = {Infinite Matrix Product States for \$(1+1)\$-Dimensional Gauge Theories},
+  author = {Dempsey, Ross and Gl{\"u}ck, Anna-Maria E. and Pufu, Silviu S. and S{\o}gaard, Benjamin T.},
+  year = 2025,
+  month = aug,
+  number = {arXiv:2508.16363},
+  eprint = {2508.16363},
+  primaryclass = {hep-th},
+  publisher = {arXiv},
+  doi = {10.48550/arXiv.2508.16363},
+  url = {http://arxiv.org/abs/2508.16363},
+  abstract = {We present a matrix product operator construction that allows us to represent the lattice Hamiltonians of (abelian or non-abelian) gauge theories in a local and manifestly translationinvariant form. In particular, we use symmetric matrix product states and introduce linkenhanced matrix product operators (LEMPOs) that can act on both the physical and virtual spaces of the matrix product states. This construction allows us to study Hamiltonian lattice gauge theories on infinite lattices. As examples, we show how to implement this method to study the massless and massive one-flavor Schwinger model and adjoint QCD2.},
+  archiveprefix = {arXiv},
+  langid = {english},
+  keywords = {Condensed Matter - Strongly Correlated Electrons,High Energy Physics - Lattice,High Energy Physics - Theory}
+}
+
 @article{devos2022,
   title = {Haldane Gap in the {{SU}}(3) [3 0 0] {{Heisenberg}} Chain},
   author = {Devos, Lukas and Vanderstraeten, Laurens and Verstraete, Frank},
@@ -150,6 +167,21 @@ @article{hauru2021
   langid = {english}
 }
 
+@article{herviou2025,
+  title = {Singularity with and without Disorder at {{Affleck-Kennedy-Lieb-Tasaki}} Points},
+  author = {Herviou, Lo{\"i}c and Rey, Anthony and Mila, Fr{\'e}d{\'e}ric},
+  year = 2025,
+  month = apr,
+  journal = {Physical Review B},
+  volume = {111},
+  number = {16},
+  pages = {L161118},
+  publisher = {American Physical Society},
+  doi = {10.1103/PhysRevB.111.L161118},
+  url = {https://link.aps.org/doi/10.1103/PhysRevB.111.L161118},
+  abstract = {The Affleck-Kennedy-Lieb-Tasaki (AKLT) point of the bilinear-biquadratic spin-1 chain is a cornerstone example of a disorder point where short-range correlations become incommensurate, and correlation lengths and momenta are nonanalytic. While the presence of singularities appears to be generic for AKLT points, we show that for a family of SU⁡({$n$}) models, the AKLT point is not a disorder point: It occurs entirely within an incommensurate phase yet the wave vector remains singular on both sides of the AKLT point. We conjecture that this possibility is generic for models where the representation is not self-conjugate and the transfer matrix non-Hermitian, while for self-conjugate representations the AKLT points remain disorder points.}
+}
+
 @article{jeckelmann2002,
   title = {Dynamical Density-Matrix Renormalization-Group Method},
   author = {Jeckelmann, Eric},
@@ -165,6 +197,54 @@ @article{jeckelmann2002
   abstract = {A density-matrix renormalization-group (DMRG) method for calculating dynamical properties and excited states in low-dimensional lattice quantum many-body systems is presented. The method is based on an exact variational principle for dynamical correlation functions and the excited states contributing to them. This dynamical DMRG is an alternate formulation of the correction vector DMRG but is both simpler and more accurate. The finite-size scaling of spectral functions is discussed and a method for analyzing the scaling of dense spectra is described. The key idea of the method is a size-dependent broadening of the spectrum. The dynamical DMRG and the finite-size scaling analysis are demonstrated on the optical conductivity of the one-dimensional Peierls-Hubbard model. Comparisons with analytical results show that the spectral functions of infinite systems can be reproduced almost exactly with these techniques. The optical conductivity of the Mott-Peierls insulator is investigated and it is shown that its spectrum is qualitatively different from the simple spectra observed in Peierls (band) insulators and one-dimensional Mott-Hubbard insulators.}
 }
 
+@misc{kirchner2025,
+  title = {Phases of {{Interacting Fibonacci Anyons}} on a {{Ladder}} at {{Half-Filling}}},
+  author = {Kirchner, Nico and Moessner, Roderich and Pollmann, Frank and {Gammon-Smith}, Adam},
+  year = 2025,
+  month = jul,
+  number = {arXiv:2507.22115},
+  eprint = {2507.22115},
+  primaryclass = {cond-mat},
+  publisher = {arXiv},
+  doi = {10.48550/arXiv.2507.22115},
+  url = {http://arxiv.org/abs/2507.22115},
+  abstract = {Two-dimensional many-body quantum systems can exhibit topological order and support collective excitations with anyonic statistics different from the usual fermionic or bosonic ones. With the emergence of these exotic point-like particles, it is natural to ask what phases can arise in interacting many-anyon systems. To study this topic, we consider the particular case of Fibonacci anyons subject to an anyonic tight-binding model with nearest-neighbor repulsion on a two-leg ladder. Focusing on the case of half-filling, for low interaction strengths an ''anyonic'' metal is found, whereas for strong repulsion, the anyons form an insulating charge-density wave. Within the latter regime, we introduce an effective one-dimensional model up to sixth order in perturbation theory arising from anyonic superexchange processes. We numerically identify four distinct phases of the effective model, which we characterize using matrix product state methods. These include both the ferro- and antiferromagnetic golden chain, a \$\textbackslash mathbb\textbraceleft Z\textbraceright\_2\$ phase, and an incommensurate phase.},
+  archiveprefix = {arXiv},
+  keywords = {Condensed Matter - Strongly Correlated Electrons,Quantum Physics}
+}
+
+@misc{linden2025,
+  title = {Spiral Renormalization Group Flow and Universal Entanglement Spectrum of the Non-{{Hermitian}} 5-State {{Potts}} Model},
+  author = {Linden, Vic Vander and Vos, Boris De and Vervoort, Kevin and Verstraete, Frank and Ueda, Atsushi},
+  year = 2025,
+  month = jul,
+  number = {arXiv:2507.14732},
+  eprint = {2507.14732},
+  primaryclass = {cond-mat},
+  publisher = {arXiv},
+  doi = {10.48550/arXiv.2507.14732},
+  url = {http://arxiv.org/abs/2507.14732},
+  abstract = {The quantum \$5\$-state Potts model is known to possess a perturbative description using complex conformal field theory (CCFT), the analytic continuation of ``theory space" to a complex plane. To study the corresponding complex fixed point on the lattice, the model must be deformed by an additional non-Hermitian term due to its complex coefficient \$\textbackslash lambda\$. Although the variational principle breaks down in this case, we demonstrate that tensor network algorithms are still capable of simulating these non-Hermitian theories. We access system sizes up to \$L = 28\$, which enable the observation of the theoretically predicted spiral flow of the running couplings. Moreover, we reconstruct the full boundary CCFT spectrum through the entanglement Hamiltonian encoded in the ground state. Our work demonstrates how tensor networks are the correct approach to capturing the approximate conformal invariance of weakly first-order phase transitions.},
+  archiveprefix = {arXiv},
+  keywords = {Condensed Matter - Strongly Correlated Electrons,Quantum Physics}
+}
+
+@misc{maertens2025,
+  title = {Real-Time Bubble Nucleation and Growth for False Vacuum Decay on the Lattice},
+  author = {Maertens, Daan and Haegeman, Jutho and Acoleyen, Karel Van},
+  year = 2025,
+  month = aug,
+  number = {arXiv:2508.13645},
+  eprint = {2508.13645},
+  primaryclass = {cond-mat},
+  publisher = {arXiv},
+  doi = {10.48550/arXiv.2508.13645},
+  url = {http://arxiv.org/abs/2508.13645},
+  abstract = {We revisit quantum false vacuum decay for the one-dimensional Ising model, focusing on the real-time nucleation and growth of true vacuum bubbles. Via matrix product state simulations, we demonstrate that for a wide range of parameters, the full time-dependent quantum state is well described by a Gaussian ansatz in terms of domain wall operators, with the associated vacuum bubble wave function evolving according to the linearized time-dependent variational principle. The emerging picture shows three different stages of evolution: an initial nucleation of small bubbles, followed by semi-classical bubble growth, which in turn is halted by the lattice phenomenon of Bloch oscillations. Furthermore, we find that the resonant bubble only plays a significant role in a certain region of parameter-space. However, when significant, it does lead to an approximately constant decay rate during the intermediate stage. Moreover, this rate is in quantitative agreement with the analytical result of Rutkevich (Phys. Rev. B 60, 14525) for which we provide an independent derivation based on the Gaussian ansatz.},
+  archiveprefix = {arXiv},
+  keywords = {Condensed Matter - Statistical Mechanics,Condensed Matter - Strongly Correlated Electrons,High Energy Physics - Lattice,High Energy Physics - Theory,Quantum Physics}
+}
+
 @article{mortier2025,
   title = {Fermionic Tensor Network Methods},
   author = {Mortier, Quinten and Devos, Lukas and Burgelman, Lander and Vanhecke, Bram and Bultinck, Nick and Verstraete, Frank and Haegeman, Jutho and Vanderstraeten, Laurens},
@@ -289,6 +369,37 @@ @article{roose2022
   langid = {english}
 }
 
+@misc{shen2025,
+  title = {Exploring the Phase Diagram of SU(2)_4 Strange Correlator},
+  author = {Shen, Ce},
+  year = 2025,
+  month = feb,
+  number = {arXiv:2502.14556},
+  eprint = {2502.14556},
+  primaryclass = {hep-th},
+  publisher = {arXiv},
+  doi = {10.48550/arXiv.2502.14556},
+  url = {http://arxiv.org/abs/2502.14556},
+  abstract = {We investigate the phase diagram of a quantum many-body system constructed via the strange correlator approach, based on the non-Abelian \$SU(2)\_4\$ fusion category, to probe topological phase transitions. Using tensor network methods, we numerically compute the half-infinite chain entanglement entropy derived from the dominant eigenvector of the transfer matrix and map the entropy across a spherical two-dimensional parameter space. Our results reveal a phase diagram significantly more complex than previously reported, including a gapless phase consistent with a conformal field theory (CFT) of central charge \$c=1\$. Critical lines separating distinct phases are identified, with one such line bounding the CFT phase exhibiting a higher central charge \$c=2\$, indicative of an unconventional critical regime.},
+  archiveprefix = {arXiv},
+  keywords = {Condensed Matter - Strongly Correlated Electrons,High Energy Physics - Theory}
+}
+
+@article{tang2025,
+  title = {Matrix Product State Fixed Points of Non-{{Hermitian}} Transfer Matrices},
+  author = {Tang, Wei and Verstraete, Frank and Haegeman, Jutho},
+  year = 2025,
+  month = jan,
+  journal = {Physical Review B},
+  volume = {111},
+  number = {3},
+  pages = {035107},
+  publisher = {American Physical Society},
+  doi = {10.1103/PhysRevB.111.035107},
+  url = {https://link.aps.org/doi/10.1103/PhysRevB.111.035107},
+  abstract = {The contraction of tensor networks is a central task in the application of tensor network methods to the study of quantum and classical many-body systems. In this paper, we investigate the impact of gauge degrees of freedom in the virtual indices of the tensor network on the contraction process, specifically focusing on boundary matrix product state methods for contracting two-dimensional tensor networks. We show that the gauge transformation can affect the entanglement structures of the eigenstates of the transfer matrix and change how the physical information is encoded in the eigenstates, which can influence the accuracy of the numerical simulation. We demonstrate this effect by looking at two different examples. First, we focus on the local gauge transformation, and analyze its effect by viewing it as an imaginary-time evolution governed by a diagonal Hamiltonian. As a specific example, we perform a numerical analysis in the classical Ising model on the square lattice. Second, we go beyond the scope of local gauge transformations and study the antiferromagnetic Ising model on the triangular lattice. The partition function of this model has two tensor network representations connected by a nonlocal gauge transformation, resulting in distinct numerical performances in the boundary matrix product state calculation.}
+}
+
 @article{ueda2024,
   title = {Chiral {{Edge States Emerging}} on {{Anyon-Net}}},
   author = {Ueda, Atsushi and Inamura, Kansei and Ohmori, Kantaro},
@@ -304,6 +415,22 @@ @article{ueda2024
   keywords = {Condensed Matter - Statistical Mechanics,Condensed Matter - Strongly Correlated Electrons,High Energy Physics - Theory}
 }
 
+@article{ueda2025,
+  title = {Chiral Edge States Emerging on Anyon-Net},
+  author = {Ueda, Atsushi and Inamura, Kansei and Ohmori, Kantaro},
+  year = 2025,
+  month = sep,
+  journal = {SciPost Physics Core},
+  volume = {8},
+  number = {3},
+  pages = {062},
+  issn = {2666-9366},
+  doi = {10.21468/SciPostPhysCore.8.3.062},
+  url = {https://www.scipost.org/SciPostPhysCore.8.3.062},
+  abstract = {SciPost Journals Publication Detail SciPost Phys. Core 8, 062 (2025) Chiral edge states emerging on anyon-net},
+  langid = {english}
+}
+
 @article{vandamme2021,
   title = {Efficient Matrix Product State Methods for Extracting Spectral Information on Rings and Cylinders},
   author = {Van Damme, Maarten and Vanhove, Robijn and Haegeman, Jutho and Verstraete, Frank and Vanderstraeten, Laurens},
@@ -394,6 +521,22 @@ @article{vanhove2022
   abstract = {We use the formalism of strange correlators to construct a critical classical lattice model in two dimensions with the Haagerup fusion category {$\mathcal{H}$}3 as input data. We present compelling numerical evidence in the form of finite entanglement scaling to support a Haagerup conformal field theory (CFT) with central charge {$c$} =2. Generalized twisted CFT spectra are numerically obtained through exact diagonalization of the transfer matrix, and the conformal towers are separated in the spectra through their identification with the topological sectors. It is further argued that our model can be obtained through an orbifold procedure from a larger lattice model with input {$Z$}⁡({$\mathcal{H}$}3), which is the simplest modular tensor category that does not admit an algebraic construction. This provides a counterexample for the conjecture that all rational CFT can be constructed from standard methods.}
 }
 
+@article{vrancken2025,
+  title = {Quantitative {{Description}} of {{Strongly Correlated Materials}} by {{Combining Downfolding Techniques}} and {{Tensor Networks}}},
+  author = {Vrancken, Daan and Ganne, Simon and Verraes, Daan and Braeckevelt, Tom and Devos, Lukas and Vanderstraeten, Laurens and Haegeman, Jutho and Van Speybroeck, Veronique},
+  year = 2025,
+  month = aug,
+  journal = {Journal of Chemical Theory and Computation},
+  volume = {21},
+  number = {16},
+  pages = {7830--7844},
+  issn = {1549-9618, 1549-9626},
+  doi = {10.1021/acs.jctc.5c00796},
+  url = {https://pubs.acs.org/doi/10.1021/acs.jctc.5c00796},
+  copyright = {https://creativecommons.org/licenses/by-nc-nd/4.0/},
+  langid = {english}
+}
+
 @article{weerda2024,
   title = {Fractional Quantum {{Hall}} States with Variational Projected Entangled-Pair States: {{A}} Study of the Bosonic {{Harper-Hofstadter}} Model},
   shorttitle = {Fractional Quantum {{Hall}} States with Variational Projected Entangled-Pair States},

docs/src/references.md

@@ -11,7 +11,15 @@ request or an issue on the [GitHub repository](https://github.com/QuantumKitHub/
 ```@bibliography
 Pages = []
 capponi2025
+dempsey2025
+herviou2025
+kirchner2025
+linden2025
 mortier2025
+maertens2025
+shen2025
+ueda2025
+vrancken2025
 ```
 ### 2024