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QUTE SIGNED

Quantum Tensor Networks and Entanglement

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Project "QUTE" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITEIT GENT 

Organization address
address: SINT PIETERSNIEUWSTRAAT 25
city: GENT
postcode: 9000
website: http://www.ugent.be

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Belgium [BE]
 Total cost 1˙927˙500 €
 EC max contribution 1˙927˙500 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2014-CoG
 Funding Scheme ERC-COG
 Starting year 2015
 Duration (year-month-day) from 2015-09-01   to  2021-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITEIT GENT BE (GENT) coordinator 1˙927˙500.00

Map

 Project objective

One of the major challenges in theoretical physics is the development of systematic methods for describing and simulating quantum many body systems with strong interactions. Given the huge experimental progress and technological potential in manipulating strongly correlated atoms and electrons, there is a pressing need for such a better theory. The study of quantum entanglement holds the promise of being a game changer for this question. By mapping out the entanglement structure of the low-energy wavefunctions of quantum spin systems on the lattice, the prototypical example of strongly correlated systems, we have found that the associated wavefunctions can be very well modeled by a novel class of variational wavefunctions, called tensor network states. Tensor networks are changing the ways in which strongly correlated systems can be simulated, classified and understood: as opposed to the usual many body methods, these tensor networks are generic and describe non-perturbative effects in a very natural way. The goal of this proposal is to advance the scope and use of tensor networks in several directions, both from the numerical and theoretical point of view. We plan to study the differential geometric character of the manifold of tensor network states and the associated nonlinear differential equations of motion on it, develop post tensor network methods in the form of effective theories on top of the tensor network vacuum, study tensor networks in the context of lattice gauge theories and topologically ordered systems, and investigate the novel insights that tensor networks are providing to the renormalization group and the holographic principle. Colloquially, we believe that tensor networks and the theory of entanglement provide a basic new vocabulary for describing strongly correlated quantum systems, and the main goal of this proposal is to develop the syntax and semantics of that new language.

 Publications

year authors and title journal last update
List of publications.
2019 Laurens Vanderstraeten, Jutho Haegeman, Frank Verstraete
Simulating excitation spectra with projected entangled-pair states
published pages: , ISSN: 2469-9950, DOI: 10.1103/PhysRevB.99.165121
Physical Review B 99/16 2020-04-03
2019 Bram Vanhecke, Jutho Haegeman, Karel Van Acoleyen, Laurens Vanderstraeten, Frank Verstraete
Scaling Hypothesis for Matrix Product States
published pages: , ISSN: 0031-9007, DOI: 10.1103/PhysRevLett.123.250604
Physical Review Letters 123/25 2020-04-03
2018 Nick Bultinck, Robijn Vanhove, Jutho Haegeman, Frank Verstraete
Global Anomaly Detection in Two-Dimensional Symmetry-Protected Topological Phases
published pages: , ISSN: 0031-9007, DOI: 10.1103/PhysRevLett.120.156601
Physical Review Letters 120/15 2020-04-03
2018 Laurens Vanderstraeten, Maarten Van Damme, Hans Peter Büchler, Frank Verstraete
Quasiparticles in Quantum Spin Chains with Long-Range Interactions
published pages: , ISSN: 0031-9007, DOI: 10.1103/PhysRevLett.121.090603
Physical Review Letters 121/9 2020-04-03
2018 Laurens Vanderstraeten, Bram Vanhecke, Frank Verstraete
Residual entropies for three-dimensional frustrated spin systems with tensor networks
published pages: , ISSN: 2470-0045, DOI: 10.1103/PhysRevE.98.042145
Physical Review E 98/4 2020-04-03
2018 M. T. Fishman, L. Vanderstraeten, V. Zauner-Stauber, J. Haegeman, F. Verstraete
Faster methods for contracting infinite two-dimensional tensor networks
published pages: , ISSN: 2469-9950, DOI: 10.1103/PhysRevB.98.235148
Physical Review B 98/23 2020-04-03
2018 Robijn Vanhove, Matthias Bal, Dominic J. Williamson, Nick Bultinck, Jutho Haegeman, Frank Verstraete
Mapping Topological to Conformal Field Theories through strange Correlators
published pages: , ISSN: 0031-9007, DOI: 10.1103/physrevlett.121.177203
Physical Review Letters 121/17 2020-04-03
2018 Nick Bultinck, Dominic J Williamson, Jutho Haegeman, Frank Verstraete
Fermionic projected entangled-pair states and topological phases
published pages: 25202, ISSN: 1751-8113, DOI: 10.1088/1751-8121/aa99cc
Journal of Physics A: Mathematical and Theoretical 51/2 2020-04-03
2018 Mario Berta, Fernando G. S. L. Brandão, Jutho Haegeman, Volkher B. Scholz, Frank Verstraete
Thermal states as convex combinations of matrix product states
published pages: , ISSN: 2469-9950, DOI: 10.1103/physrevb.98.235154
Physical Review B 98/23 2020-04-03
2019 Alexis Schotte, Jose Carrasco, Bram Vanhecke, Laurens Vanderstraeten, Jutho Haegeman, Frank Verstraete, Julien Vidal
Tensor-network approach to phase transitions in string-net models
published pages: , ISSN: 2469-9950, DOI: 10.1103/physrevb.100.245125
Physical Review B 100/24 2020-04-03
2018 V. Zauner-Stauber, L. Vanderstraeten, J. Haegeman, I. P. McCulloch, F. Verstraete
Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries
published pages: , ISSN: 2469-9950, DOI: 10.1103/PhysRevB.97.235155
Physical Review B 97/23 2020-04-03
2020 Laurens Lootens, Robijn Vanhove, Jutho Haegeman, Frank Verstraete
Galois Conjugated Tensor Fusion Categories and Nonunitary Conformal Field Theory
published pages: , ISSN: 0031-9007, DOI: 10.1103/physrevlett.124.120601
Physical Review Letters 124/12 2020-04-03
2019 Laurens Vanderstraeten, Jutho Haegeman, Frank Verstraete
Tangent-space methods for uniform matrix product states
published pages: , ISSN: 2590-1990, DOI: 10.21468/SciPostPhysLectNotes.7
SciPost Physics Lecture Notes 2020-04-03
2018 V. Zauner-Stauber, L. Vanderstraeten, M. T. Fishman, F. Verstraete, J. Haegeman
Variational optimization algorithms for uniform matrix product states
published pages: , ISSN: 2469-9950, DOI: 10.1103/PhysRevB.97.045145
Physical Review B 97/4 2020-04-03
2017 Michaël Mariën, Jutho Haegeman, Paul Fendley, Frank Verstraete
Condensation-driven phase transitions in perturbed string nets
published pages: 9, ISSN: 2469-9950, DOI: 10.1103/PhysRevB.96.155127​
Physical Review B 96/15 2020-03-17
2017 M. Bal, M. Mariën, J. Haegeman, F. Verstraete
Renormalization Group Flows of Hamiltonians Using Tensor Networks
published pages: , ISSN: 0031-9007, DOI: 10.1103/PhysRevLett.118.250602
Physical Review Letters 118/25 2020-03-17
2017 J.I. Cirac, D. Pérez-García, N. Schuch, F. Verstraete
Matrix product density operators: Renormalization fixed points and boundary theories
published pages: 100-149, ISSN: 0003-4916, DOI: 10.1016/j.aop.2016.12.030
Annals of Physics 378 2020-03-17
2017 Jutho Haegeman, Frank Verstraete, Damian Draxler, Vid Stojevic, Ignacio Cirac, Tobias Osborne
Quantum Gross-Pitaevskii Equation
published pages: 18, ISSN: 2542-4653, DOI: 10.21468/SciPostPhys.3.1.006
SciPost Physics 3/1 2020-03-17
2017 Laurens Vanderstraeten, Michaël Mariën, Jutho Haegeman, Norbert Schuch, Julien Vidal, Frank Verstraete
Bridging Perturbative Expansions with Tensor Networks
published pages: , ISSN: 0031-9007, DOI: 10.1103/PhysRevLett.119.070401
Physical Review Letters 119/7 2020-03-17
2017 Boye Buyens, Simone Montangero, Jutho Haegeman, Frank Verstraete, Karel Van Acoleyen
Finite-representation approximation of lattice gauge theories at the continuum limit with tensor networks
published pages: 23, ISSN: 2470-0010, DOI: 10.1103/PhysRevD.95.094509
Physical Review D 95/9 2020-03-17
2017 J Ignacio Cirac, David Perez-Garcia, Norbert Schuch, Frank Verstraete
Matrix product unitaries: structure, symmetries, and topological invariants
published pages: 83105, ISSN: 1742-5468, DOI: 10.1088/1742-5468/aa7e55
Journal of Statistical Mechanics: Theory and Experiment 2017/8 2020-03-17
2017 Jutho Haegeman and Frank Verstraete
Diagonalizing Transfer Matrices and Matrix product operators: a medley of exact and computational methods
published pages: , ISSN: 1947-5454, DOI: 10.1146/annurev-conmatphys-031016-025507
Annual review of condensed matter physics 8/1 2020-03-17
2016 M. Bal, M. M. Rams, V. Zauner, J. Haegeman, F. Verstraete
Matrix product state renormalization
published pages: 14, ISSN: 2469-9950, DOI: 10.1103/PhysRevB.94.205122
Physical Review B 94/20 2020-03-17
2016 Boye Buyens , Jutho Haegeman, Henri Verschelde, Frank Verstraete and Karel Van Acoleyen
Confinement and string breaking for QED2 in the Hamiltonian picture
published pages: 32, ISSN: 2160-3308, DOI: 10.1103/PhysRevX.6.041040
Physical review X 6/4 2020-03-17
2015 Laurens Vanderstraeten, Michaël Mariën, Frank Verstraete, Jutho Haegeman
Excitations and the tangent space of projected entangled-pair states
published pages: , ISSN: 1098-0121, DOI: 10.1103/PhysRevB.92.201111
Physical Review B 92/20 2020-03-17
2016 Jutho Haegeman, Christian Lubich, Ivan Oseledets, Bart Vandereycken, Frank Verstraete
Unifying time evolution and optimization with matrix product states
published pages: 10, ISSN: 2469-9950, DOI: 10.1103/PhysRevB.94.165116
Physical Review B 94/16 2020-03-17
2016 V Zauner, D Draxler, L Vanderstraeten, J Haegeman, F Verstraete
Symmetry breaking and the geometry of reduced density matrices
published pages: 113033, ISSN: 1367-2630, DOI: 10.1088/1367-2630/18/11/113033
New Journal of Physics 18/11 2020-03-17
2016 Marek M Rams, Valentin Zauner, Matthias Bal, Jutho Haegeman and Frank Verstraete
Truncating an exact matrix product state for the XY model: transfer matrix and its renormalization
published pages: 13, ISSN: 1098-0121, DOI: 10.1103/PhysRevB.92.235150
Physical review B 92/23 2020-03-17
2016 Laurens Vanderstraeten, Jutho Haegeman, Frank Verstraete, Didier Poilblanc
Quasiparticle interactions in frustrated Heisenberg chains
published pages: 8, ISSN: 2469-9950, DOI: 10.1103/PhysRevB.93.235108
Physical Review B 93/23 2020-03-17
2016 Laurens Vanderstraeten, Jutho Haegeman, Philippe Corboz, Frank Verstraete
Gradient methods for variational optimization of projected entangled-pair states
published pages: 14, ISSN: 2469-9950, DOI: 10.1103/PhysRevB.94.155123
Physical Review B 94/15 2020-03-17
2016 Karel Van Acoleyen, Nick Bultinck, Jutho Haegeman, Michael Marien, Volkher B. Scholz, Frank Verstraete
Entanglement of Distillation for Lattice Gauge Theories
published pages: , ISSN: 0031-9007, DOI: 10.1103/PhysRevLett.117.131602
Physical Review Letters 117/13 2020-03-17
2016 Boye Buyens, Frank Verstraetet and Karel Van Acoleyen
Hamiltonian simulation of the Schwinger model at finite temperature
published pages: 33, ISSN: 2470-0010, DOI: 10.1103/PhysRevD.94.085018
Physical Review D 94 2020-03-17
2015 Laurens Vanderstraeten, Frank Verstraete, Jutho Haegeman
Scattering particles in quantum spin chains
published pages: , ISSN: 1098-0121, DOI: 10.1103/PhysRevB.92.125136
Physical Review B 92/12 2020-03-17
2017 Damian Draxler, Jutho Haegeman , Frank Verstraete and Matteo Rizzi
Continuous matrix product states with periodic boundary conditions and an application to atomtronics
published pages: , ISSN: 2469-9950, DOI: 10.1103/PhysRevB.95.045145
Physical Review B 95/4 2020-03-17
2017 Nick Bultinck, Dominic J. Williemson, Jutho Haegeman and Frank Verstraete
Fermionic matrix product states and one-dimensional topological phases
published pages: 24, ISSN: 2469-9950, DOI: 10.1103/PhysRevB.95.075108
Physical Review B 95/7 2020-03-17
2017 Nick Bultinck, Michaël Mariën, D.J. Williamson, M.B. Sahinoglu, Jutho Haegeman and Frank Verstraete
Anyons and matrix product operator algebras
published pages: , ISSN: 0003-4916, DOI: 10.1016/j.aop.2017.01.004
Annals of Physics 378 2020-03-17
2016 Ling Wang, Zheng-Cheng Gu, Frank Verstraete and Xiao-Gang Wen
Tensor-product state approach to spin-1/2 square J₁-J2 antiferromagnetic Heisenberg model: evidence for deconfined quantum criticality
published pages: 6, ISSN: 2469-9950, DOI: 10.1103/PhysRevB.94.075143
Physical review B 94/7 2020-03-17
2016 Michaël Mariën, Koenraad Audenaert, Karel van Acoleyen and Frank Verstraete
Entanglement rates and the stability of the area law of the entanglement entropy
published pages: 35-73, ISSN: 0010-3616, DOI: 10.1007/s00220-016-2709-5
Communications in Mathematical Physics 346/1 2020-03-17
2016 Boye Buyens , Jutho Haegeman , Frank Verstraete and Karel Van Acoleyen
Tensor networks for gauge field theories
published pages: 7, ISSN: 1824-8039, DOI:
Proceeding of science 280 2020-03-17

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