Lycee Saint Louis

Saint-Michel-sur-Orge, France

Lycee Saint Louis

Saint-Michel-sur-Orge, France
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Filippone M.,CNRS Pierre Aigrain Laboratory | Dusuel S.,Lycee Saint Louis | Vidal J.,University Pierre and Marie Curie
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2011

We consider a set of fully connected spin models that display first- or second-order transitions and for which we compute the ground-state entanglement in the thermodynamical limit. We analyze several entanglement measures (concurrence, Rényi entropy, and negativity) and show that, in general, discontinuous transitions lead to a jump of these quantities at the transition point. Interestingly, we also find examples where this is not the case. © 2011 American Physical Society.


Schulz M.D.,TU Dortmund | Dusuel S.,Lycee Saint Louis | Orus R.,Max Planck Institute of Quantum Optics | Vidal J.,University Pierre and Marie Curie | Schmidt A.P.,TU Dortmund
New Journal of Physics | Year: 2012

We studied the robustness of a generalized Kitaev's toric code with ℤN degrees of freedom in the presence of local perturbations. For N = 2, this model reduces to the conventional toric code in a uniform magnetic field. A quantitative analysis was performed for the perturbed ℤ3 toric code by applying a combination of high-order series expansions and variational techniques. We found strong evidence for first-and second-order phase transitions between topologically ordered and polarized phases. Most interestingly, our results also indicate the existence of topological multi-critical points in the phase diagram. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.


Dusuel S.,Lycee Saint Louis | Kamfor M.,TU Dortmund | Kamfor M.,University Pierre and Marie Curie | Orus R.,University of Queensland | And 3 more authors.
Physical Review Letters | Year: 2011

We investigate the stability of the topological phase of the toric code model in the presence of a uniform magnetic field by means of variational and high-order series expansion approaches. We find that when this perturbation is strong enough, the system undergoes a topological phase transition whose first- or second-order nature depends on the field orientation. When this transition is of second order, it is in the Ising universality class except for a special line on which the critical exponent driving the closure of the gap varies continuously, unveiling a new topological universality class. © 2011 American Physical Society.


Schulz M.D.,TU Dortmund | Schulz M.D.,University Pierre and Marie Curie | Dusuel S.,Lycee Saint Louis | Schmidt K.P.,TU Dortmund | Vidal J.,University Pierre and Marie Curie
Physical Review Letters | Year: 2013

We examine the zero-temperature phase diagram of the two-dimensional Levin-Wen string-net model with Fibonacci anyons in the presence of competing interactions. Combining high-order series expansions around three exactly solvable points and exact diagonalizations, we find that the non-Abelian doubled Fibonacci topological phase is separated from two nontopological phases by different second-order quantum critical points, the positions of which are computed accurately. These trivial phases are separated by a first-order transition occurring at a fourth exactly solvable point where the ground-state manifold is infinitely many degenerate. The evaluation of critical exponents suggests unusual universality classes. © 2013 American Physical Society.


Kamfor M.,TU Dortmund | Kamfor M.,University Pierre and Marie Curie | Dusuel S.,Lycee Saint Louis | Schmidt K.P.,TU Dortmund | Vidal J.,University Pierre and Marie Curie
Physical Review B - Condensed Matter and Materials Physics | Year: 2011

We consider noninteracting fermions on the honeycomb lattice in the presence of a magnetic vortex superlattice. It is shown that depending on the superlattice periodicity, a gap may open at zero energy. We derive an expression of the gap in the small-flux limit but the main qualitative features are found to be valid for arbitrary fluxes. This study provides an original example of a metal-insulator transition induced by a strongly modulated magnetic field in graphene. At the same time, our results directly apply to Kitaev's honeycomb model in a vortex superlattice. © 2011 American Physical Society.


Schulz M.D.,TU Dortmund | Schulz M.D.,University Pierre and Marie Curie | Dusuel S.,Lycee Saint Louis | Misguich G.,CEA Saclay Nuclear Research Center | And 2 more authors.
Physical Review B - Condensed Matter and Materials Physics | Year: 2014

We consider the string-net model on the honeycomb lattice for Ising anyons in the presence of a string tension. This competing term induces a nontrivial dynamics of the non-Abelian anyonic quasiparticles and may lead to a breakdown of the topological phase. Using high-order series expansions and exact diagonalizations, we determine the robustness of this doubled Ising phase, which is found to be separated from two gapped phases. An effective quantum dimer model emerges in the large tension limit, giving rise to two different translation symmetry-broken phases. Consequently, we obtain four transition points, two of which are associated with first-order transitions whereas the two others are found to be continuous and provide examples of recently proposed Bose condensation for anyons. © 2014 American Physical Society.


Kamfor M.,TU Dortmund | Kamfor M.,University Pierre and Marie Curie | Dusuel S.,Lycee Saint Louis | Vidal J.,University Pierre and Marie Curie | Schmidt K.P.,TU Dortmund
Physical Review B - Condensed Matter and Materials Physics | Year: 2014

Dynamical correlation functions of the toric code in a uniform magnetic field are studied inside the topological phase, in the small-field limit. Such an experimentally measurable quantity displays rich field-dependent features that can be understood via the interplay of the kinetics and the interaction of the anyonic excitations. In particular, it is sensitive to the two-quasiparticle bound states that are present in the spectrum for a wide range of magnetic fields. Interestingly, such collective modes can even constitute the lowest-energy excitations of the system. © 2014 American Physical Society.


Schulz M.D.,University of Minnesota | Dusuel S.,Lycee Saint Louis | Vidal J.,University Pierre and Marie Curie
Physical Review B - Condensed Matter and Materials Physics | Year: 2015

We study a string-net ladder in the presence of a string tension. Focusing on the simplest non-Abelian anyon theory with a quantum dimension larger than two, we determine the phase diagram and find a Russian doll spectrum featuring size-independent energy levels as well as highly degenerate zero-energy eigenstates. At the self-dual points, we compute the gap exactly by using a mapping onto the Temperley-Lieb chain. These results are in stark contrast with the ones obtained for Fibonacci or Ising theories. © 2015 American Physical Society.


Wilms J.,University of Vienna | Vidal J.,University Pierre and Marie Curie | Verstraete F.,University of Vienna | Dusuel S.,Lycee Saint Louis
Journal of Statistical Mechanics: Theory and Experiment | Year: 2012

We study the finite-temperature behavior of the Lipkin-Meshkov-Glick model with a focus on correlation properties as measured by the mutual information. The latter, which quantifies the amount of both classical and quantum correlations, is computed exactly in the two limiting cases of vanishing magnetic field and vanishing temperature. For all other situations, numerical results provide evidence of a finite mutual information at all temperatures except at criticality. There, it diverges as the logarithm of the system size, with a prefactor that can take only two values, depending on whether the critical temperature vanishes or not. Our work provides a simple example in which the mutual information appears as a powerful tool to detect finite-temperature phase transitions, contrary to entanglement measures such as the concurrence. © 2012 IOP Publishing Ltd and SISSA.


Dusuel S.,Lycee Saint Louis | Vidal J.,University Pierre and Marie Curie
Physical Review B - Condensed Matter and Materials Physics | Year: 2015

We propose a simple mean-field ansatz to study phase transitions from a topological phase to a trivial phase. We probe the efficiency of this approach by considering the string-net model in the presence of a string tension for any anyon theory. Such a perturbation is known to be responsible for a deconfinement-confinement phase transition which is well described by the present variational setup. We argue that mean-field results become exact in the limit of large total quantum dimension. © 2015 American Physical Society. ©2015 American Physical Society.

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