Symmetries and Entanglement in Quantum Matter

Project Information

SEQUAM

Grant agreement ID: 863476

DOI

10.3030/863476

EC signature date 16 December 2019

Start date 1 October 2020

End date 30 September 2026

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 953 375,00

EU contribution

€ 1 953 375,00

Coordinated by

UNIVERSITAT WIEN
Austria

CORDIS provides links to public deliverables and publications of HORIZON projects.

Links to deliverables and publications from FP7 projects, as well as links to some specific result types such as dataset and software, are dynamically retrieved from OpenAIRE .

Publications

Peer reviewed articles (30)

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

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

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

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

"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

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

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

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

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

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

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

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

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

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

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

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

Other (14)

Gauging Quantum Phases: A Matrix Product State Approach

Author(s): David Blanik, José Garre-Rubio, Norbert Schuch
Published in: arXiv, Issue 2504.14380, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2504.14380

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: arXiv, Issue 2411.03680, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2411.03680

Positive bias makes tensor-network contraction tractable

Author(s): Jiaqing Jiang, Jielun Chen, Norbert Schuch, Dominik Hangleiter
Published in: arXiv, Issue 2410.05414, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2410.05414

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: arXiv, Issue 2204.05940, 2022
Publisher: arXiv
DOI: 10.48550/arxiv.2204.05940

Multi wavefunction overlap and multi entropy for topological ground states in (2+1) dimensions

Author(s): Bowei Liu, Junjia Zhang, Shuhei Ohyama, Yuya Kusuki, Shinsei Ryu
Published in: arXiv, Issue 2410.08284, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2410.08284

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

The product structure of MPS-under-permutations

Author(s): Marta Florido-Llinàs, Álvaro M. Alhambra, Rahul Trivedi, Norbert Schuch, David Pérez-García, J. Ignacio Cirac
Published in: arXiv, Issue 2410.19541, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2410.19541

Stable and efficient differentiation of tensor network algorithms

Author(s): Anna Francuz, Norbert Schuch, Bram Vanhecke
Published in: arXiv, 2023
Publisher: arXiv
DOI: 10.48550/arxiv.2311.11894

MPS Stability and the Intersection Property

Author(s): José Garre-Rubio, Alex Turzillo, András Molnár
Published in: arXiv, Issue 2501.17109, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2501.17109

Systematic construction of stabilizer codes via gauging abelian boundary symmetries

Author(s): Bram Vancraeynest-De Cuiper, José Garre-Rubio
Published in: arXiv, Issue 2410.09044, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2410.09044

Preparation Circuits for Matrix Product States by Classical Variational Disentanglement

Author(s): Refik Mansuroglu, Norbert Schuch
Published in: arXiv, Issue 2504.21298, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2504.21298

Detection of 2D SPT Order with Partial Symmetries

Author(s): Alex Turzillo, Naren Manjunath, Jose Garre-Rubio
Published in: arXiv, Issue 2503.04510, 2025
Publisher: arXiv
DOI: 10.48550/arxiv.2503.04510

Classifying symmetric and symmetry-broken spin chain phases with anomalous group actions

Author(s): Jose Garre Rubio, Andras Molnar, Yoshiko Ogata
Published in: arXiv, Issue 2403.18573, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2403.18573

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: arXiv, Issue 2407.03073, 2024
Publisher: arXiv
DOI: 10.48550/arxiv.2407.03073

Conference proceedings (2)

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