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Spectral gaps in interacting quantum systems

Total Cost €


EC-Contrib. €






Project "GAPS" data sheet

The following table provides information about the project.


Organization address
city: MADRID
postcode: 28040

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 Spain [ES]
 Project website
 Total cost 1˙462˙750 €
 EC max contribution 1˙462˙750 € (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


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

Interactions in a many body quantum system are encoded in a Hamiltonian, where the physical intuition that particles can only interact with those which are closeby is formally imposed as a local structure in the Hamiltonian, and homogeneity in space is imposed by a translational invariant structure on a given regular lattice in one, two or three dimensions. The first main aim of this proposal is to characterize the existence of a uniform (with the system size) lower bound on the gap between the two lowest eigenvalues of a given local translational invariant Hamiltonian.

There are many reasons which motivate this study, coming from different fields, and hence many potential applications. We will concentrate here on those coming from quantum information theory and from condensed matter physics and mainly, as the second main aim of this proposal, on classifying the different possible quantum phases arising in this type of models.


year authors and title journal last update
List of publications.
2018 Christoph Sünderhauf, David Pérez-García, David A. Huse, Norbert Schuch, J. Ignacio Cirac
Localization with random time-periodic quantum circuits
published pages: , ISSN: 2469-9950, DOI: 10.1103/physrevb.98.134204
Physical Review B 98/13 2020-03-24
2020 Yilun Yang, Sofyan Iblisdir, J. Ignacio Cirac, Mari Carmen Bañuls
Probing Thermalization through Spectral Analysis with Matrix Product Operators
published pages: , ISSN: 0031-9007, DOI: 10.1103/physrevlett.124.100602
Physical Review Letters 124/10 2020-03-24
2019 Andrea Coser, David Pérez-García
Classification of phases for mixed states via fast dissipative evolution
published pages: 174, ISSN: 2521-327X, DOI: 10.22331/q-2019-08-12-174
Quantum 3 2020-03-24
2019 Aleksander M. Kubicki, Carlos Palazuelos, David Pérez-García
Resource Quantification for the No-Programing Theorem
published pages: , ISSN: 0031-9007, DOI: 10.1103/PhysRevLett.122.080505
Physical Review Letters 122/8 2020-03-24
2018 Andras Molnar, José Garre-Rubio, David Pérez-García, Norbert Schuch, J Ignacio Cirac
Normal projected entangled pair states generating the same state
published pages: 113017, ISSN: 1367-2630, DOI: 10.1088/1367-2630/aae9fa
New Journal of Physics 20/11 2020-03-24
2018 Gemma De las Cuevas, Norbert Schuch, David Perez-Garcia, J. Ignacio Cirac
Continuum limits of matrix product states
published pages: , ISSN: 2469-9950, DOI: 10.1103/physrevb.98.174303
Physical Review B 98/17 2020-03-24
2019 Chris N. Self, Johannes Knolle, Sofyan Iblisdir, Jiannis K. Pachos
Thermally induced metallic phase in a gapped quantum spin liquid: Monte Carlo study of the Kitaev model with parity projection
published pages: , ISSN: 2469-9950, DOI: 10.1103/physrevb.99.045142
Physical Review B 99/4 2020-03-24
2020 Matthew Cha, Pieter Naaijkens, Bruno Nachtergaele
On the Stability of Charges in Infinite Quantum Spin Systems
published pages: 219-264, ISSN: 0010-3616, DOI: 10.1007/s00220-019-03630-1
Communications in Mathematical Physics 373/1 2020-03-24
2019 José Garre-Rubio, Sofyan Iblisdir
Local order parameters for symmetry fractionalization
published pages: 113016, ISSN: 1367-2630, DOI: 10.1088/1367-2630/ab4fff
New Journal of Physics 21/11 2020-03-24
2019 Michael J. Kastoryano, Angelo Lucia, David Perez-Garcia
Locality at the Boundary Implies Gap in the Bulk for 2D PEPS
published pages: 895-926, ISSN: 0010-3616, DOI: 10.1007/s00220-019-03404-9
Communications in Mathematical Physics 366/3 2020-03-24
2018 Marcus Huber, Ludovico Lami, Cécilia Lancien, Alexander Müller-Hermes
High-Dimensional Entanglement in States with Positive Partial Transposition
published pages: , ISSN: 0031-9007, DOI: 10.1103/PhysRevLett.121.200503
Physical Review Letters 121/20 2020-03-24
2020 Kohtaro Kato, Pieter Naaijkens
An entropic invariant for 2D gapped quantum phases
published pages: 85302, ISSN: 1751-8113, DOI: 10.1088/1751-8121/ab63a5
Journal of Physics A: Mathematical and Theoretical 53/8 2020-03-24
2019 Juan Ignacio Cirac, José Garre-Rubio, David Pérez-García
Mathematical open problems in projected entangled pair states
published pages: 579-599, ISSN: 1139-1138, DOI: 10.1007/s13163-019-00318-x
Revista Matemática Complutense 32/3 2020-03-24
2017 Chris N. Self, Jiannis K. Pachos, James R. Wootton, Sofyan Iblisdir
Conformal energy currents on the edge of a topological superconductor
published pages: , ISSN: 2469-9950, DOI: 10.1103/PhysRevB.95.115141
Physical Review B 95/11 2019-07-23
2017 Andrea Coser, Cristiano De Nobili, Erik Tonni
A contour for the entanglement entropies in harmonic lattices
published pages: 314001, ISSN: 1751-8113, DOI: 10.1088/1751-8121/aa7902
Journal of Physics A: Mathematical and Theoretical 50/31 2019-07-23
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 2019-07-23
2015 Fernando G. S. L. Brandão, Toby S. Cubitt, Angelo Lucia, Spyridon Michalakis, David Perez-Garcia
Area law for fixed points of rapidly mixing dissipative quantum systems
published pages: 102202, ISSN: 0022-2488, DOI: 10.1063/1.4932612
Journal of Mathematical Physics 56/10 2019-07-23
2016 Carlos Fernández-González, Roger S. K. Mong, Olivier Landon-Cardinal, David Pérez-García, Norbert Schuch
Constructing topological models by symmetrization: A projected entangled pair states study
published pages: , ISSN: 2469-9950, DOI: 10.1103/PhysRevB.94.155106
Physical Review B 94/15 2019-07-23
2016 Cristiano De Nobili, Andrea Coser, Erik Tonni
Entanglement negativity in a two dimensional harmonic lattice: area law and corner contributions
published pages: 83102, ISSN: 1742-5468, DOI: 10.1088/1742-5468/2016/08/083102
Journal of Statistical Mechanics: Theory and Experiment 2016/8 2019-07-23
2016 G. De las Cuevas, T. S. Cubitt, J. I. Cirac, M. M. Wolf, D. Pérez-García
Fundamental limitations in the purifications of tensor networks
published pages: 71902, ISSN: 0022-2488, DOI: 10.1063/1.4954983
Journal of Mathematical Physics 57/7 2019-07-23
2015 Toby S. Cubitt, David Perez-Garcia, Michael M. Wolf
Undecidability of the spectral gap
published pages: 207-211, ISSN: 0028-0836, DOI: 10.1038/nature16059
Nature 528/7581 2019-07-23
2018 Angela Capel, Angelo Lucia, David Perez-Garcia
Superadditivity of Quantum Relative Entropy for General States
published pages: 1-1, ISSN: 0018-9448, DOI: 10.1109/TIT.2017.2772800
IEEE Transactions on Information Theory 2019-07-23
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 2019-07-23
2017 José Garre-Rubio, Sofyan Iblisdir, David Pérez-García
Symmetry reduction induced by anyon condensation: A tensor network approach
published pages: , ISSN: 1098-0121, DOI: 10.1103/PhysRevB.96.155123
Physical Review B 96/15 2019-07-23
2017 Gemma De las Cuevas, J. Ignacio Cirac, Norbert Schuch, David Perez-Garcia
Irreducible forms of matrix product states: Theory and applications
published pages: 121901, ISSN: 0022-2488, DOI: 10.1063/1.5000784
Journal of Mathematical Physics 58/12 2019-07-23
2018 Johannes Bausch, Toby S. Cubitt, Angelo Lucia, David Perez-Garcia, Michael M. Wolf
Size-driven quantum phase transitions
published pages: 19-23, ISSN: 0027-8424, DOI: 10.1073/pnas.1705042114
Proceedings of the National Academy of Sciences 115/1 2019-07-23
2018 Ángela Capel, Angelo Lucia, David Pérez-García
Quantum conditional relative entropy and quasi-factorization of the relative entropy
published pages: , ISSN: 1751-8113, DOI: 10.1088/1751-8121/aae4cf
Journal of Physics A: Mathematical and Theoretical 2019-07-23

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