Condensed Matter Theory Group

We develop new techniques in many-body theory for the description of exotic quantum phases that are relevant for the study of cold atomic systems and the simulation of topological quantum matter. We are also interested in the treatment of non-equilibrium phenomena like decoherence and quantum transport and applications to working quantum devices.


Name Category Office Ext E-mail
Jorge Dukelsky Research Professor 123, 140 941137
José González Research Professor 123, 118 941118
Rafael A. Molina Tenured Scientist 123, 131 941128
Enrique Benito Matías PhD. Student 123, 132 941129
Álvaro Rubio PhD. Student 123, 132 941129

Former members of the group

María Concepción Pulido Postdoc 2016-2017
Jordi Mur-Petit JAE Postdoc 2012-2015
Carlos Essebag Associated researcher 2007-2015
Daniel Huerga PhD. Student 2009-2014
Nicolae Sandulescu Sabbatical 2012-2013
Anders Mathias Lunde Postdoc 2013
Pablo San José JAE Postdoc 2009-2012
Armando Relaño Postdoc Juan de la Cierva and JAE 2006-2011
Stefan Rombouts Postdoc Marie Curie 2008-2010
Beatriz Errea PhD. Student 2004-2008


We are a theoretical group doing research in different topics in condensed matter physics and the applications of quantum mechanics.

Twisted bilayer graphene

We have put forward a comprehensive microscopic theory which places the origin of the superconductivity of twisted graphene bilayers in the highly anisotropic Fermi line developed at the small twist angles.

Topological semimetals

We have studied the surface states of topological semimetals using a description based on exceptional points once the crystal momentum is complexified. But we also study bulk properties based on a field-theoretical description.

Quantum thermodynamics

Quantum fluctuation relations applied to out-of-equilibrium processes in quantum systems, thermalization, and excited state phase transitions.

Quantum transport through nanostructures

Quantum transport through disordered systems in the presence of ac fields. Electronic Aharanov-Bohm interferometers.

Development of new methods for the many-body problem in quantum mechanics

We are currently developing new methods beyond mean-field for attacking the many-body problem, specially using methods based on the density matrix.

Quantum chaos

Applications of quantum chaos from nuclear physics to cold molecules or condensed matter. But also fundamental developments in the statistical analysis of spectra and Random Matrix Theory.


2021, 2020, 2019, 2018, 2017, 2016, 2015, 2014, 2013, 2012, 2011, 2010









  • Lattice Scars: Surviving in an open discrete billiard
    V. Fernández-Hurtado, J. Mur-Petit, J.J. García-Ripoll, R.A. Molina
    New J. Phys. 16, 035005 (2014)
  • Collective modes of a trapped ion-dipole system:Towards measuring, controlling and entangling electric dipoles with atomic ions
    J. Mur-Petit, J.J. García-Ripoll
    Appl. Phys. B 114, 283-294 (2014)
  • Chiral bound states in the continuum
    J. Mur-Petit, R.A. Molina
    Phys. Rev. B 90, 035434 (2014)
  • The Lipkin-Meshkov-Glick model from the perspective of the SU(1,1) Richardson-Gaudin models
    S. H. Lerma, J. Dukelsky
    J. Phys.: Conf. Ser. 492, 012013 (2014)
  • Density matrix embedding from broken symmetry lattice mean fields
    I. W. Bulik, G. E. Scuseria, J. Dukelsky
    Physical Review B 89, 035140 (2014)
  • Chiral phases of two-dimensional hard-core bosons with frustrated ring exchange
    D. Huerga, J. Dukelsky, N. Laflorencie, G. Ortiz
    Physical Review B 89, 094401 (2014)
  • Quasiparticle coupled cluster theory for pairing interactions
    T. M. Henderson, G. E. Scuseria, J. Dukelsky, A. Signoracci, T. Duguet
    Physical Review C 89, 054305 (2014)
  • Phase stabilization of a frequency comb using multi-pulse quantum interferometry
    A. Cadarso, J. Mur-Petit, J.J. García-Ripoll
    Phys. Rev. Lett. 112, 073603 (2014)
  • Marginal Fermi liquid versus excitonic instability in 3D Dirac semimetals
    J. González
    Physical Review B 90, 121107(R) (2014)
  • Rippling transition from electron-induced condensation of curvature field in graphene
    J. González
    Physical Review B 90, 165402 (2014)

  • 2013


    • Non-Abelian gauge potentials in graphene bilayers
      P. San-José, J. González and F. Guinea
      Physical Review Letters 108, 216802 (2012)
    • Electron self-energy effects on chiral symmetry breaking in graphene
      J. González
      Physical Review B 85, 085420 (2012)
    • Higher-order renormalization of graphene many-body theory
      J. González
      Journal of High Energy Physics 08, 27 (2012)
    • AC Josephson effect in finite-length nanowire junctions with Majorana modes
      P. San-José, E. Prada, R. Aguado
      Physical Review Letters 108, 257001 (2012)
    • Laser-induced quantum pumping in graphene
      P. San-José, E. Prada, H. Schomerus, S. Kohler
      Applied Physics Letters 101, 153506 (2012)
    • Transport spectroscopy of N-S nanowire junctions with Majorana fermions
      E. Prada, P. San-José, R. Aguado
      Physical Review B 86, 180503 (2012)
    • Scattering phase thorugh quantum dots: Emergence of universal behavior
      R.A. Molina, R.A. Jalabert, D. Weinmann, Ph. Jacquod
      Phys. Rev. Lett. 108, 076803 (2012)
    • Quartet condensation and isovector pairing correlations in N=Z Nuclei
      N. Sandliescu, D. Negrea, J. Dukelsky, C.W. Johnson
      Phys. Rev. C 85, 061303(R) (2012)
    • Integrable Richardson-Gaudin models in mesoscopic physics
      J. Dukelsky
      J. Phys.: Conf. Ser. 338 (2012) 012023
    • Excited state quantum phase transitions and chaos in the Dicke model
      P. P&ecute;rez-Fernández, A. Relaño, P. Cejnar, J.M. Arias, J. Dukelsky and J.E. Garcí­a-Ramos
      AIP Conference Proceedings, 1488 (2012) 318
    • Decoherence and quantum quench: their relationship with excited state quantum phase transitions
      J. E. Garcí­a-Ramos, J. M. Arias, P. Cejnar, J. Dukelsky, P. Pérez-Fernández, y A. Relaño
      AIP Conference Proceedings, 1488 (2012) 309
    • New realizations of the Richardson-Gaudin models in nuclear physics: the hyperbolic model
      J. Dukelsky and S. Lerma
      AIP Conference Proceedings, 1488 (2012) 182
    • Isovector pairing and quartet condensation in N=Z Nuclei
      N. Sandulescu, D. Negrea, J. Dukelsky, C.W. Johnson
      AIP Conference Proceedings, 1498 (2012) 359
    • Embedding method for the scattering phase in strongly correlated quantum dots
      R.A. Molina, P. Schmitteckert, D. Weinmann, R.A. Jalabert, Ph. Jacquod
      J. Phys.: Conf. Ser. 338 (2012) 012011
    • Apunts de Física 2010
      J. Mur
      Revista de Fí­sica 4(8), 31-33 (2012)
    • Towards a molecular ion qubit
      J. Mur-Petit, J. Pérez-RÃíos, J. Campos- Martínez, M. I. Hernández, S. Willitsch, J. J. Garcí­a-Ripoll
      Architecture and Design of Molecule Logic Gates and Atom Circuits, N. Lorente and C. Joaquim (eds.), Proceedings of the 2nd AtMol European Workshop, Springer (Heidelberg), Advances in Atom and Single-Molecule Machines Series (2012). ISBN: 978-3642331367.


    • Electron-induced rippling in graphene
      P. San-José, J. González and F. Guinea
      Physical Review Letters 106, 045502 (2011)
    • Progress in modeling graphene: The novel features of this material
      F. Guinea, M. A. H. Vozmediano, M. P. López-Sancho and J. González
      Advanced Materials 23, 5324 (2011)
    • Gate driven adiabatic quantum pumping in graphene
      E. Prada, P. San-Jos&ecute;, H. Schomerus
      Solid State Communications 151, 1065 (2011)
    • Band topology and the quantum spin Hall effect in bilayer graphene
      E. Prada, P. San-Joé, L. Brey, H. A. Fertig
      Solid State Communications 151, 1075 (2011)
    • Single-parameter pumping in graphene
      P. San-José, E. Prada, S. Kohler, H. Schomerus
      Physical Review B 84, 155408 (2011)
    • Many-Body quantum chaos: Recent developments and applications to nuclei
      J.M.G. Gómez, K. Kar, V.K.B. Kota, R.A. Molina, A. Relaño, and J. Retamosa
      Physics Reports 499, 103 (2011)
    • Recent results on quantum chaos and its applications to atomic nuclei
      J.M.G. Gómez, E. Faleiro, L. Muñoz, R.A. Molina, A. Relaño, and J. Retamosa
      Journal of Physics: Conference Series 267, 012061 (2011)
    • Tailored particle current in an optical lattice by a weak time-symmetric harmonic potential
      J. Santos, R.A. Molina, J. Ortigoso, M. Rodríguez
      Physical Review A 84, 023614 (2011)
    • Quantum quench influenced by an excited-state phase transition
      P. Pérez Fernández, P. Cejnar, J.M. Arias, J. Dukelsky, J.E. García-Ramos, A. Relano
      Physical Review A 83, 033802 (2011)
    • Excited-state phase transition and onset of chaos in quantum optical models
      P. P&ecuate;rez Fernández, A. Relaño, J.M. Arias, P. Cejnar J. Dukelsky, J.E. Garcia-Ramos
      Physical Review E 83, 046208 (2011)
    • Comment on "Fermi-Bose Mixtures near Broad Interspecies Feshbach. Resonances"
      J. Dukelsky, C. Esebbag, P. Schuck, T. Suzuki
      Physical Review Letters 106, 129601 (2011)
    • Integrable two-channel px+ipy-wave model of a superfluid.
      S. Lerma H., S. M. A. Rombouts, J. Dukelsky,G. Ortiz
      Physical Review B 84, 100503(R) (2011).
    • Exactly solvable pairing Hamiltonian for heavy nuclei.
      J. Dukelsky, S. Lerma H., L. M. Robledo, R. Rodriguez-Guzman, and S. M. A. Rombouts.
      Physical Review B 84, 100503(R) (2011).
    • Richardson-Gaudin models: the hyperbolic family.
      J. Dukelsky, S. Rombouts, G. Ortiz
      Journal of Physics: Conference Series 321, 012001 (2011).


    • Pairing in 4-component fermion systems: The bulk limit of SU(4)-symmetric Hamiltonians
      G. F. Bertsch, J. Dukelsky, B. Errea and C. Esebbag
      Annals of Physics 325, 1340 (2010)
    • Prediction of resonant all-electric spin pumping with spin-orbit coupling
      V. Brosco, M. Jerger, P. San-José, G. Zarand, A. Shnirman and G. Schön
      Physical Review B 82, 041309(R) (2010)
    • Renormalization group approach to chiral symmetry breaking in graphene
      J. González
      Physical Review B 82, 155404 (2010)
    • Graphene wormholes: A condensed matter illustration of Dirac fermions in curved space
      J. González and J. Herrero
      Nuclear Physics B 825, 426 (2010)
    • Controlling the conductance statistics of quantum wires by driving ac fields
      V. A. Gopar, R. A. Molina
      Physical Review B 81, 195415 (2010)
    • Interplay of Tomonaga-Luttinger liquids and superconductive phase in carbon nanotubes
      J. Haruyama, J. González, E. Perfetto, E. Einarson, S. Maruyama and H. Shinohara
      Europhysics Letters 89, 27003 (2010)
    • Phase diagram of the Heisenberg antiferromagnet with four-spin interactions
      L. Isaev, G. Ortiz and J. Dukelsky
      Journal of Physics: Condensed Matter 22, 016006 (2010)
    • Comment on a Quantum phase transition in the four-spin exchange antiferromagnet
      L. Isaev, G. Ortiz, J. Dukelsky
      Physical Review B 82, 136401 (2010)
    • Extended van Hove singularity and superconducting instability in doped graphene
      J. L. McChesney, A. Bostwick, T. Ohta, T. Seyller, K. Horn, J. González and E. Rotenberg
      Physical Review Letters 104, 136803 (2010)
    • Perspectives on 1/f noise in quantum chaos
      R. A. Molina, A. Relaño, J. Retamosa, L. Muñoz, E. Faleiro and J. M. G. Gómez
      Journal of Physics: Conference Series 239, 012001 (2010)
    • Connection between decoherence and excited state quantum phase transitions
      P. Pérez-Fernández, A. Relaño, J. M. Arias, J. E. García-Ramos, J. Dukelsky
      AIP Conference Proceedings 1231, 233-234 (2010)
    • Singular elastic strains and magnetoconductance of suspended graphene
      E. Prada, P. San-José, G. León, M. M. Fogler and F. Guinea
      Physical Review B 81, 161402(R) (2010)
    • Zero Landau Level in Folded Graphene Nanoribbons
      E. Prada, P. San-José, L. Brey
      Physical Review Letters 105, 106802 (2010)
    • Quantum phase diagram of the integrable px+ipy fermionic superfluid
      S. M. A. Rombouts, J. Dukelsky, G. Ortiz
      Physical Review B 82, 224510 (2010)
    • Color-charge separation in trapped SU(3) fermionic atoms
      T. Ulbricht, R. A. Molina, R. Thomale, P. Schmitteckert
      Physical Review A 82, 011603(R) (2010)


    • August 3, 2021
      Two Ph.D Contracts offered for thesis work on superconducting and topological phases on Moiré systems. Download announcement
    • January 1, 2019
      José González in collaboration with Tobias Stauber from ICMM, proposes an explanation for the superconducting properties of twisted bilayer graphene Press release (in Spanish)
    • May 22, 2018
      Rafael Molina in collaboration with researches in Oxford has derived new formulas for the description of quantum fluctuations in non-equilibrium processes when there are conserved quantities. These results may be of great importance for improving the design of quantum machines, using the presence of these conserved quantities for improving their efficiency.Press release (in Spanish)
    • March 8, 2017
      A work about diffusion of wave packets in quantum interferometers, with the participation of Rafael Molina (IEM--CSIC) has been highlighted in the JPhys+, the Journal of Physics news and views blog. The article studies the diffusion of an electronic wave packet through a quantum interferometer and is a collaboration with researchers at Harvard University and the Zuse Institut in Berlin. The large scale simulations needed rely on the computational power of Graphic Processing Units (GPU).

    Superconductivity in twisted bilayer graphene

    The experimental observation of superconductivity in twisted bilayer graphene has been one of the most outstanding discoveries carried out during the last years in the context of condensed matter physics. It has certainly attracted much attention as the first instance in which a material made purely of carbon has proven to be superconducting, in the absence of any chemical doping. Moreover, this discovery represents a change of paradigm when looking for materials with unconventional superconductivity, as chemical complexity is replaced here by the structural complexity of the twisted bilayers, which become superconducting near the so-called magic twist angle, when the period of the resulting moiré superlattice is above 10 nanometers. We have put forward a comprehensive microscopic theory which places the origin of the superconductivity of twisted graphene bilayers in the highly anisotropic Fermi line developed at the small twist angles where they become superconducting. Our theoretical construction can be considered as a variant of the so-called Kohn-Luttinger mechanism, which was devised as an alternative route to superconductivity starting from a purely repulsive Coulomb interaction. Usually, the Kohn-Luttinger instability takes place at extremely low energy scales but, in twisted bilayer graphene, it is amplified by the doubling and subsequent strong coupling of the van Hove singularities of the electronic spectrum as the magic angle is approached, leading to quite extended saddle points in the highest valence band. In these circumstances, we have found that the highly anisotropic screening along the Fermi line is able to induce an attractive channel in the effective electron-electron interaction. This is the seed required to trigger a superconducting instability, which takes place in our model at a low-energy scale which is consistent with the critical temperatures observed in the experiments. Moreover, we have also shown that the large density of electron-hole excitations from the given Fermi line is able to develop a spin-density-wave instability adjacent to the superconducting instability, for doping levels close to the van Hove singularity in the spectrum. This may also explain the existence of the insulating phase observed at half-filling of the moiré superlattice, which seems to play the role of parent phase for the superconducting regime, and it is the other key ingredient in the puzzling resemblance of the phase diagram of the twisted bilayers to that of such strongly correlated systems as the high-Tc superconductors.

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