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Saint-Michel-sur-Orge, France

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

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. Source

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

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. Source

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

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. Source

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

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. Source

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

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. Source

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