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Investigation of the many-body localized phase

par Webmaster - 7 octobre 2016

Toutes les versions de cet article : English , français

PhD advisors : Fabien Alet, Nicolas Laflorencie

This condensed matter theory PhD proposal deals with the study of the Many-Body Localized (MBL) phase, a recently discovered new phase of matter induced by the interplay between disorder and strong interactions between quantum particles. While studies of Anderson localization have now acquired a certain degree of maturity, the field of many-body localization is still in its infancy, and is probably one of the most exciting open problems in condensed matter theory, with one to three preprints every week.

Recent results indicate that the MBL phase hosts new features, which contradict several paradigms in quantum and statistical physics : (i) MBL states do not equilibrate thermally, in contrast with the large majority of quantum states, (ii) they have a very low entanglement (area law) instead of the usual volume law, (iii) they depart from the Mermin-Wagner theorem : they can host long-range, possibly topological, order even in one dimension at finite temperature. Disorder helps ordering ! (iv) MBL states can retain initial information up to infinite time. Due to these unique properties, MBL states are promising candidates for self-correcting quantum memories. Very recently, experiments have provided evidence for the first time for the existence of the MBL phase in cold-atomic systems.

Most of the understanding of the many-body localization physics comes from phenomenological approaches, with limited numerical evidence. Very important questions remain open : what is the nature (universality class ?) of the many-body localization phase transition ? Can one obtain many-body localized phase without disorder ? Is MBL restricted to one-dimensional sys- tems ? Can we quantitatively compare theory and experiments ? Can we capture the physics of MBL states in a unified framework ?

This PhD proposal aims at addressing these challenging questions, by adding solid evidence based on exact results to the existing phenomenology. Due to the broad nature of the topic, the PhD student will have to use tools coming from different fields : many-body techniques, quantum information and chaos, localization physics etc. The student will develop in particular new numerical approaches of either condensed matter (exact diagonalization, quantum Monte Carlo) or quantum information (tensor network) type. Semi-analytical approaches (Bethe lattice) can also be considered. In such a fresh and rapidly moving field, there is a lot of room for creativity and it is likely that the student will participate in developing new methods to tackle these questions.

The applicant will have a solid background in quantum mechanics and statistical physics. The PhD thesis will take place in the condensed matter theory group of the Laboratoire de Physique Théorique in Toulouse. Our team has recently developed new specific methods at the forefront of the numerical study of MBL, and the student will likely benefit from these advances.

Reference :

Extended slow dynamical regime close to the many-body localization transition, David J. Luitz, Nicolas Laflorencie, and Fabien Alet, Phys. Rev. B 93, 060201(R) (2016)

Many-body localization edge in the random-field Heisenberg chain, David J. Luitz, Nicolas Laflorencie, Fabien Alet, Phys. Rev. B 91, 081103 (2015)

Contact : Fabien Alet, Chargé de Recherches CNRS, Laboratoire de Physique Théorique, Toulouse Nicolas Laflorencie, Chargé de Recherches CNRS, Laboratoire de Physique Théorique, Toulouse

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