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GAPS SIGNED

Spectral gaps in interacting quantum systems

Total Cost €

EC-Contrib. €

Partnership

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Outcomes and
results

GAPS project word cloud

Explore the words cloud of the GAPS project. It provides you a very rough idea of what is the project "GAPS" about.

gap local mainly formally existence eigenvalues lattice interactions imposed closeby size lowest dimensions regular models lower first condensed encoded space phases interact particles translational classifying physical quantum intuition body theory structure invariant hence hamiltonian homogeneity bound arising uniform physics concentrate motivate coming

Project "GAPS" data sheet

The following table provides information about the project.

Coordinator	UNIVERSIDAD COMPLUTENSE DE MADRID Organization address address: AVENIDA DE SENECA 2 city: MADRID postcode: 28040 website: http://www.ucm.es 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	http://www.gapsproject.com
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

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	UNIVERSIDAD COMPLUTENSE DE MADRID UNIVERSIDAD COMPLUTENSE DE MADRID Organization address address: AVENIDA DE SENECA 2 city: MADRID postcode: 28040 website: http://www.ucm.es contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	ES (MADRID)	coordinator	1˙462˙750.00

Map

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.

Publications

List of publications.
year	authors and title	journal	last update
2018	Christoph SÃ¼nderhauf, David PÃ©rez-GarcÃa, 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 BaÃ±uls 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 PÃ©rez-GarcÃa 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 PÃ©rez-GarcÃa 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, JosÃ© Garre-Rubio, David PÃ©rez-GarcÃa, 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	JosÃ© 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, CÃ©cilia Lancien, Alexander MÃ¼ller-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, JosÃ© Garre-Rubio, David PÃ©rez-GarcÃa Mathematical open problems in projected entangled pair states published pages: 579-599, ISSN: 1139-1138, DOI: 10.1007/s13163-019-00318-x	Revista MatemÃ¡tica 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. PÃ©rez-GarcÃa, 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. BrandÃ£o, 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 FernÃ¡ndez-GonzÃ¡lez, Roger S. K. Mong, Olivier Landon-Cardinal, David PÃ©rez-GarcÃa, 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. PÃ©rez-GarcÃa 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	JosÃ© Garre-Rubio, Sofyan Iblisdir, David PÃ©rez-GarcÃa 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	Ãngela Capel, Angelo Lucia, David PÃ©rez-GarcÃa 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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