Symmetries and Entanglement in Quantum Matter

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Publications

Detecting emergent continuous symmetries at quantum criticality

Author(s): Mingru Yang, Bram Vanhecke, Norbert Schuch
Published in: Physical Review Letters, Issue Vol. 131, Iss. 3, 2023, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/physrevlett.131.036505

Gauging quantum states with non-anomalous matrix product operator symmetries

Author(s): Ilya Kull; Jose Garre-Rubio
Published in: Physical Review B, Issue Vol. 107, Iss. 7, 2023, ISSN 2469-9969
Publisher: American Physical Society

Validating phase-space methods with tensor networks in two-dimensional spin models with power-law interactions

Author(s): Sean R. Muleady, Mingru Yang, Steven R. White, Ana Maria Rey
Published in: Physical Review Letters, Issue Vol. 131, Iss. 15, 2023, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/physrevlett.131.150401

Gauging quantum phases: A matrix product state approach

Author(s): David Blanik, José Garre-Rubio, Norbert Schuch
Published in: Physical Review B, Issue 112, 2025, ISSN 2469-9950
Publisher: American Physical Society (APS)
DOI: 10.1103/gkh9-lgrk

Stable and efficient differentiation of tensor network algorithms

Author(s): Anna Francuz, Norbert Schuch, Bram Vanhecke
Published in: Physical Review Research, Issue 7, 2025, ISSN 2643-1564
Publisher: American Physical Society (APS)
DOI: 10.1103/physrevresearch.7.013237

A Hierarchy of Spectral Gap Certificates for Frustration-Free Spin Systems

Author(s): Kshiti Sneh Rai, Ilya Kull, Patrick Emonts, Jordi Tura, Norbert Schuch, Flavio Baccari
Published in: Quantum, Issue 10, 2026, Page(s) 2065, ISSN 2521-327X
Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
DOI: 10.22331/q-2026-04-13-2065

Internal structure of gauge-invariant projected entangled pair states

Author(s): David Blanik, José Garre-Rubio, András Molnár, Erez Zohar
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 58, 2025, Page(s) 065301, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/adae83

Entanglement Order Parameters and Critical Behavior for Topological Phase Transitions and Beyond

Author(s): Mohsin Iqbal, Norbert Schuch
Published in: Physical Review X, Issue Vol. 11, Iss. 4, 2021, Page(s) article nr. 041014, ISSN 2160-3308
Publisher: American Physical Society
DOI: 10.1103/physrevx.11.041014

Two-dimensional bialgebras and quantum groups: algebraic structures and tensor network realizations

Author(s): José Garre-Rubio, András Molnár, Germán Sierra
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 59, 2026, Page(s) 095202, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ae414d

On tensor network representations of the (3+1)d toric code

Author(s): Clement Delcamp, Norbert Schuch
Published in: Quantum, Issue Vol. 5, 2021, Page(s) 604-635, ISSN 2521-327X
Publisher: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
DOI: 10.22331/q-2021-12-16-604

Tangent Space Excitation Ansatz for Quantum Circuits

Author(s): Ji-Yao Chen, Bochen Huang, D. L. Zhou, Norbert Schuch, Chenfeng Cao, Muchun Yang
Published in: Physical Review Letters, Issue 136, 2026, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/k2lc-v1hn

"Entanglement spectra of nonchiral topological (<mml:math xmlns:mml=""http://www.w3.org/1998/Math/MathML""><mml:mn>2</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:math>)-dimensional phases with strong time-reversal symmetry breaking, Li-Haldane state counting, and PEPS"

Author(s): Mark J. Arildsen, Norbert Schuch, Andreas W. W. Ludwig
Published in: Physical Review B, Issue 108, 2023, ISSN 2469-9950
Publisher: American Physical Society (APS)
DOI: 10.1103/physrevb.108.245150

Tangent Space Generators of Matrix Product States and Exact Floquet Quantum Scars

Author(s): Marko Ljubotina, Elena Petrova, Norbert Schuch, Maksym Serbyn
Published in: PRX Quantum, Issue 5, 2024, ISSN 2691-3399
Publisher: American Physical Society (APS)
DOI: 10.1103/prxquantum.5.040311

Fractionalization of subsystem symmetries in two dimensions

Author(s): David T. Stephen, Arpit Dua, José Garre-Rubio, Dominic J. Williamson, Michael Hermele
Published in: Physical Review B, Issue Vol. 106, Iss. 8, 2022, ISSN 2469-9969
Publisher: American Physical Society
DOI: 10.1103/physrevb.106.085104

Symmetry Protected Topological Order in Open Quantum Systems

Author(s): Caroline de Groot, Alex Turzillo, Norbert Schuch
Published in: Quantum, Issue Vol. 6, 2022, Page(s) 856, ISSN 2521-327X
Publisher: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
DOI: 10.22331/q-2022-11-10-856

Fractional domain wall statistics in spin chains with anomalous symmetries

Author(s): José Garre-Rubio, Norbert Schuch
Published in: SciPost Physics, Issue 18, 2025, ISSN 2542-4653
Publisher: Stichting SciPost
DOI: 10.21468/scipostphys.18.2.043

Planning with tensor networks based on active inference

Author(s): Samuel T Wauthier, Tim Verbelen, Bart Dhoedt, Bram Vanhecke
Published in: Machine Learning: Science and Technology, Issue 5, 2024, Page(s) 045012, ISSN 2632-2153
Publisher: IOP Publishing
DOI: 10.1088/2632-2153/ad7571

Matrix Product Operator Algebras I: Representations of Weak Hopf Algebras and Projected Entangled Pair States

Author(s): Andras Molnar, Alberto Ruiz-de-Alarcón, José Garre-Rubio, Norbert Schuch, J. Ignacio Cirac, David Pérez-García
Published in: Communications in Mathematical Physics, Issue 407, 2026, ISSN 0010-3616
Publisher: Springer Verlag
DOI: 10.1007/s00220-026-05670-w

Robustness of critical U(1) spin liquids and emergent symmetries in tensor networks

Author(s): Henrik Dreyer, Laurens Vanderstraeten, Ji-Yao Chen, Ruben Verresen, Norbert Schuch
Published in: Physical Review B, Issue 109, 2024, ISSN 2469-9950
Publisher: American Physical Society (APS)
DOI: 10.1103/physrevb.109.195161

Anyonic symmetry fractionalization in symmetry enriched topological phases

Author(s): José Garre-Rubio, Yoshiko Ogata
Published in: Journal of Mathematical Physics, Issue 67, 2026, ISSN 0022-2488
Publisher: American Institute of Physics
DOI: 10.1063/5.0291274

Hyperinvariant spin network states — an AdS/CFT model from first principles

Author(s): Fynn Otto, Refik Mansuroglu, Norbert Schuch, Otfried Gühne, Hanno Sahlmann
Published in: Journal of High Energy Physics, Issue 2026, 2026, ISSN 1029-8479
Publisher: Institute of Physics Publishing
DOI: 10.1007/jhep06(2026)145

Generating function for tensor network diagrammatic summation

Author(s): Wei-Lin Tu; Wei-Lin Tu; Huan-Kuang Wu; Norbert Schuch; Naoki Kawashima; Ji-Yao Chen
Published in: Physical Review B, Issue Vol. 103, Iss. 20, 2021, Page(s) article nr. 205155, ISSN 2469-9950
Publisher: American Physical Society
DOI: 10.1103/physrevb.103.205155

The Product Structure of Matrix Product States under Permutations

Author(s): Marta Florido-Llinàs, Álvaro M. Alhambra, Rahul Trivedi, Norbert Schuch, David Pérez-García, J. Ignacio Cirac
Published in: PRX Quantum, Issue 6, 2025, ISSN 2691-3399
Publisher: American Physical Society (APS)
DOI: 10.1103/8sbs-t24w

Locality optimization for parent Hamiltonians of tensor networks

Author(s): Giuliano Giudici, J. Ignacio Cirac, Norbert Schuch
Published in: Physical Review B, Issue Vol. 106, Iss. 3, 2022, ISSN 2469-9969
Publisher: American Physical Society
DOI: 10.1103/physrevb.106.035109

Matrix product operator algebras II: phases of matter for 1D mixed states

Author(s): Alberto Ruiz-de-Alarcón, José Garre-Rubio, András Molnár, David Pérez-García
Published in: Letters in Mathematical Physics, Issue 114, 2024, ISSN 1573-0530
Publisher: Springer Nature B.V.
DOI: 10.1007/s11005-024-01778-z

From gauging to duality in one-dimensional quantum lattice models

Author(s): Bram Vancraeynest-De Cuiper, José Garre-Rubio, Frank Verstraete, Kevin Vervoort, Dominic J. Williamson, Laurens Lootens
Published in: SciPost Physics, Issue 20, 2026, ISSN 2542-4653
Publisher: Stichting SciPost
DOI: 10.21468/scipostphys.20.4.113

Lower Bounds on Ground-State Energies of Local Hamiltonians through the Renormalization Group

Author(s): Ilya Kull, Norbert Schuch, Ben Dive, Miguel Navascués
Published in: Physical Review X, Issue 14, 2024, ISSN 2160-3308
Publisher: American Physical Society
DOI: 10.1103/physrevx.14.021008

Matrix-product operator dualities in integrable lattice models

Author(s): Yuan Miao, Andras Molnar, Nick G Jones
Published in: Journal of Physics A: Mathematical and Theoretical, Issue 59, 2026, Page(s) 305002, ISSN 1751-8113
Publisher: Institute of Physics Publishing
DOI: 10.1088/1751-8121/ae880b

Tensor Networks Can Resolve Fermi Surfaces

Author(s): Quinten Mortier, Norbert Schuch, Frank Verstraete, Jutho Haegeman
Published in: Physical Review Letters, Issue Vol. 129, Iss. 20, 2022, ISSN 1079-7114
Publisher: American Physical Society
DOI: 10.1103/physrevlett.129.206401

Entanglement spectrum as a diagnostic of chirality of topological spin liquids: Analysis of SU(3) projected entangled pair states

Author(s): Mark J. Arildsen, Ji-Yao Chen, Norbert Schuch, Andreas W. W. Ludwig
Published in: Physical Review B, Issue 110, 2024, ISSN 2469-9950
Publisher: American Physical Society (APS)
DOI: 10.1103/physrevb.110.235147

On the stability of topological order in tensor network states

Author(s): Dominic J. Williamson, Clement Delcamp, Frank Verstraete, Norbert Schuch
Published in: Physical Review B, Issue Vol. 104, Iss. 23, 2021, Page(s) article nr. 235151, ISSN 2469-9950
Publisher: American Physical Society
DOI: 10.1103/physrevb.104.235151

Mapping between Morita-equivalent string-net states with a constant depth quantum circuit

Author(s): Laurens Lootens, Bram Vancraeynest-De Cuiper, Norbert Schuch, Frank Verstraete
Published in: Physical Review B, Issue Vol. 105, Iss. 8, 2022, Page(s) article nr. 085130, ISSN 2469-9950
Publisher: American Physical Society
DOI: 10.1103/physrevb.105.085130

Generating Function for Projected Entangled-Pair States

Author(s): Wei-Lin Tu, Laurens Vanderstraeten, Norbert Schuch, Hyun-Yong Lee, Naoki Kawashima, Ji-Yao Chen
Published in: PRX Quantum, Issue 5, 2024, ISSN 2691-3399
Publisher: American Physical Society (APS)
DOI: 10.1103/prxquantum.5.010335

MPS Stability and the Intersection Property

Author(s): José Garre-Rubio, Alex Turzillo, András Molnár
Published in: Annales Henri Poincaré, 2026, ISSN 1424-0637
Publisher: Birkhauser Verlag
DOI: 10.1007/s00023-025-01650-3

Matrix product states and projected entangled pair states: Concepts, symmetries, theorems

Author(s): Ignacio Cirac, David Perez-Garcia, Norbert Schuch, Frank Verstraete
Published in: Reviews of Modern Physics, Issue Vol. 93, Iss. 4, 2021, Page(s) article nr. 045003, ISSN 0034-6861
Publisher: American Physical Society
DOI: 10.1103/revmodphys.93.045003

Preparation and verification of tensor network states

Author(s): Esther Cruz; Flavio Baccari; Jordi Tura; Norbert Schuch; J. Ignacio Cirac
Published in: Physical Review Research, Issue Vol. 4, Iss. 2, 2022, ISSN 2643-1564
Publisher: American Physical Society
DOI: 10.1103/physrevresearch.4.023161

Higher structures on boundary conformal manifolds: Higher Berry phase and boundary conformal field theory

Author(s): Yichul Choi, Hyunsoo Ha, Dongyeob Kim, Yuya Kusuki, Shuhei Ohyama, Shinsei Ryu
Published in: Physical Review D, Issue 113, 2026, ISSN 2470-0010
Publisher: American Physical Society (APS)
DOI: 10.1103/z8pw-8ckx

Classifying phases protected by matrix product operator symmetries using matrix product states

Author(s): José Garre-Rubio, Laurens Lootens, András Molnár
Published in: Quantum, Issue Vol.7, 2023, Page(s) 927, ISSN 2521-327X
Publisher: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
DOI: 10.22331/q-2023-02-21-927

Systematic construction of stabilizer codes via gauging abelian boundary symmetries

Author(s): Bram Vancraeynest-De Cuiper, José Garre-Rubio
Published in: Quantum, Issue 9, 2025, Page(s) 1852, ISSN 2521-327X
Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
DOI: 10.22331/q-2025-09-08-1852

Sign Problem in Tensor-Network Contraction

Author(s): Jielun Chen, Jiaqing Jiang, Dominik Hangleiter, Norbert Schuch
Published in: PRX Quantum, Issue 6, 2025, ISSN 2691-3399
Publisher: American Physical Society (APS)
DOI: 10.1103/prxquantum.6.010312

Preparation circuits for matrix product states by classical variational disentanglement

Author(s): Refik Mansuroglu, Norbert Schuch
Published in: Physical Review A, Issue 113, 2026, ISSN 2469-9926
Publisher: American Physical Society (APS)
DOI: 10.1103/7x2g-twkl

Fractional chiral hinge insulator

Author(s): Anna Hackenbroich, Ana Hudomal, Ana Hudomal, Norbert Schuch, B. Andrei Bernevig, Nicolas Regnault
Published in: Physical Review B, Issue Vol. 103, Iss. 16, 2021, Page(s) article nr. L161110, ISSN 2469-9950
Publisher: American Physical Society
DOI: 10.1103/physrevb.103.l161110

Detection of two-dimensional symmetry protected topological order with partial symmetries

Author(s): Alex Turzillo, Naren Manjunath, José Garre-Rubio
Published in: Physical Review B, Issue 112, 2025, ISSN 2469-9950
Publisher: American Physical Society (APS)
DOI: 10.1103/mfwg-svcp

Classifying Symmetric and Symmetry-Broken Spin Chain Phases with Anomalous Group Actions

Author(s): José Garre Rubio, Andras Molnar, Yoshiko Ogata
Published in: Annales Henri Poincaré, 2026, ISSN 1424-0637
Publisher: Birkhauser Verlag
DOI: 10.1007/s00023-026-01717-9

Beating the Natural Grover Bound for Low-Energy Estimation and State Preparation

Author(s): Harry Buhrman, Sevag Gharibian, Zeph Landau, François Le Gall, Norbert Schuch, Suguru Tamaki
Published in: Physical Review Letters, Issue 135, 2025, ISSN 0031-9007
Publisher: American Physical Society
DOI: 10.1103/29qw-bssx

Symmetries and local transformations of translationally invariant Matrix Product States

Author(s): Martin Hebenstreit, David Sauerwein, Andras Molnar, J. Ignacio Cirac, Barbara Kraus
Published in: Physical Review A, Issue Vol. 105, Iss. 3, 2022, Page(s) article nr. 032424, ISSN 2469-9926
Publisher: American Physical Society
DOI: 10.1103/physreva.105.032424

"Multiwavefunction overlap and multientropy for topological ground states in ( <mml:math xmlns:mml=""http://www.w3.org/1998/Math/MathML""> <mml:mn>2</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:math> ) dimensions"

Author(s): Bowei Liu, Junjia Zhang, Shuhei Ohyama, Yuya Kusuki, Shinsei Ryu
Published in: Physical Review B, Issue 112, 2025, ISSN 2469-9950
Publisher: American Physical Society (APS)
DOI: 10.1103/tjcf-yryh

On two-dimensional tensor network group symmetries

Author(s): José Garre-Rubio, András Molnár
Published in: New Journal of Physics, Issue 27, 2025, Page(s) 104510, ISSN 1367-2630
Publisher: Institute of Physics Publishing
DOI: 10.1088/1367-2630/ae124f

Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters

Author(s): Wen-Tao Xu, Norbert Schuch
Published in: Physical Review B, Issue Vol. 104, Iss. 15, 2021, Page(s) article nr. 155119, ISSN 2469-9950
Publisher: American Physical Society
DOI: 10.1103/physrevb.104.155119

Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states

Author(s): Wen-Tao Xu; Jose Garre-Rubio; Norbert Schuch
Published in: Physical Review B, Issue Vol. 106, Iss. 20, 2022, ISSN 2469-9969
Publisher: American Physical Society
DOI: 10.1103/physrevb.106.205139

Direct Equivalence between Dynamics of Quantum Walks and Coupled Classical Oscillators

Author(s): Lilith Zschetzsche, Refik Mansuroglu, András Molnár, Norbert Schuch
Published in: arXiv, Issue 2512.03681, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2512.03681

Non-abelian quantum double models from iterated gauging

Author(s): David Blanik, José Garre-Rubio
Published in: arXiv, Issue 2512.08749, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2512.08749

Trading Mathematical for Physical Simplicity: Bialgebraic Structures in Matrix Product Operator Symmetries

Author(s): Yuhan Liu, Andras Molnar, Xiao-Qi Sun, Frank Verstraete, Kohtaro Kato, Laurens Lootens
Published in: arXiv, Issue 2509.03600, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2509.03600

Spin models with critical ground space degeneracy from Lie algebra relations

Author(s): Andras Molnar, Efekan Kökcü, Norbert Schuch, Bojko N. Bakalov
Published in: arXiv, Issue 2608.20849, 2026
Publisher: arXiv
DOI: 10.48550/arxiv.2608.20849

The local characterization of global tensor network eigenstates

Author(s): José Garre Rubio, András Molnár, Norbert Schuch, Frank Verstraete
Published in: arXiv, Issue 2603.28349, 2026
Publisher: arXiv
DOI: 10.48550/arxiv.2603.28349

Implicit differentiation of tensor network algorithms

Author(s): Lander Burgelman, Anna Francuz, Paul Brehmer, Lukas Devos, Jutho Haegeman, Frank Verstraete, Bram Vanhecke
Published in: arXiv, Issue 2607.15030, 2026
Publisher: arXiv
DOI: 10.48550/arxiv.2607.15030

Complexity of Quadratic Bosonic Hamiltonian Simulation: BQP-Completeness and PostBQP-Hardness

Author(s): Lilith Zschetzsche, Refik Mansuroglu, Norbert Schuch
Published in: arXiv, Issue 2603.26561, 2026
Publisher: arXiv
DOI: 10.48550/arxiv.2603.26561

Parameterized families of 2+1d G-cluster states

Author(s): Shuhei Ohyama, Kansei Inamura
Published in: arXiv, Issue 2601.08616, 2026
Publisher: arXiv
DOI: 10.48550/arxiv.2601.08616

PEPSKit.jl: A Julia package for projected entangled-pair state simulations

Author(s): Paul Brehmer, Lander Burgelman, Zheng-Yuan Yue, Gleb Fedorovich, Jutho Haegeman, Lukas Devos
Published in: arXiv, Issue 2605.19960, 2026
Publisher: arXiv
DOI: 10.48550/arxiv.2605.19960

Simple Hamiltonians for Matrix Product State models

Author(s): Norbert Schuch, Andras Molnar, David Perez-Garcia
Published in: arXiv, Issue 2503.10767, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2503.10767

Generalized cluster states in 2+1d: non-invertible symmetries, interfaces, and parameterized families

Author(s): Kansei Inamura, Shuhei Ohyama
Published in: arXiv, Issue 2601.08615, 2026
Publisher: arXiv
DOI: 10.48550/arxiv.2601.08615

Parameterized Families of Toric Code Phase: em-duality family and higher-order anyon pumping

Author(s): Shuhei Ohyama, Takamasa Ando, Ryan Thorngren
Published in: arXiv, Issue 2605.03891, 2026
Publisher: arXiv
DOI: 10.48550/arxiv.2605.03891

Lower Bounds on Spectral Gaps of Parent Hamiltonians via Tensor Networks

Author(s): Milán Ádám Rozmán, András Molnár, Norbert Schuch
Published in: arXiv, Issue 2607.19078, 2026
Publisher: arXiv
DOI: 10.48550/arxiv.2607.19078

Positive Bias Makes Tensor-Network Contraction Tractable

Author(s): Jiaqing Jiang, Jielun Chen, Norbert Schuch, Dominik Hangleiter
Published in: Proceedings of the 57th Annual ACM Symposium on Theory of Computing, 2025, Page(s) 471-482
Publisher: ACM
DOI: 10.1145/3717823.3718105

Tensor networks for active inference with discrete observation spaces

Author(s): Samuel T. Wauthier, Bram Vanhecke, Tim Verbelen, Bart Dhoedt
Published in: Machine Learning and the Physical Sciences workshop, part of NeurIPS2022, the 36th Conference on Neural Information Processing Systems, 2022
Publisher: NeurIPS2022

Learning Generative Models for Active Inference using Tensor Networks

Author(s): Samuel T. Wauthier, Bram Vanhecke, Tim Verbelen, Bart Dhoedt
Published in: IWAI2022 (ECML/PKDD 2022 workshop), 2022
Publisher: arXiv / IWAI 2022: 3rd International Workshop on Active Inference (ECML/PKDD workshop)
DOI: 10.48550/arxiv.2208.08713

A Simpler Exponential-Time Approximation Algorithm for MAX-\(k\)-SAT

Author(s): Harry Buhrman, Sevag Gharibian, Zeph Landau, François Le Gall, Norbert Schuch, Suguru Tamaki
Published in: 2026 SIAM Symposium on Simplicity in Algorithms (SOSA), 2026, Page(s) 247-253
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/1.9781611978964.18

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