Lundi 6 décembre 2021
IRMA
This is a colloquium in Physics and Mathematics, organised biannually in Strasbourg by a group of scientists from IRMA, ISIS and IPCMS.
This second session is devoted to Many-body localization.
Organizers : N. Anantharaman, R. Côte, S. Klevtsov, Y. Le Floch, C. Tauber, M. Vogel, X. Zeng (IRMA) — G. Pupillo, J. Schachenmayer (ISIS) — P.-A. Hervieux, R. Jalabert, G. Manfredi, G. Weick, D. Weinmann (IPCMS)
Speakers :
- Dmitry Abanin (Université de Genève)
- François Huveneers (Paris-Dauphine)
Location : Salle de conferences IRMA (presentation of the EU digital covid certificate is required)
BBB link to follow the seminar : https://webconf.math.cnrs.fr/b/dre-nm6-42q
For practical and other questions please contact the organizers.
Abstracts
Slides from Abanin : Link to download.
Slides from Huveneers : Link to download.
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Lundi 6 décembre 2021
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09:30
Dmitry Abanin, Université de Genève
Ergodicity, entanglement, and many-body localization
Abstract: We are used to describing systems of many particles by statistical mechanics. However, recently it was realized that the basic postulate of statistical mechanics – ergodicity -- breaks down in many-body localized systems, where disorder prevents particle transport and thermalization. In this talk, I will describe the theory of the many-body localized (MBL) phase, based on new insights from quantum entanglement. I will argue that, in contrast to ergodic systems, MBL eigenstates are not highly entangled, but rather obey so-called area law, typical of ground states in gapped systems. I will use this fact to show that MBL phase is characterized by an infinite number of emergent local conservation laws, in terms of which the Hamiltonian acquires a universal form. Turning to the experimental implications, I will show that MBL systems exhibit a universal response to quantum quenches: surprisingly, entanglement shows logarithmic in time growth, reminiscent of glasses, while local observables exhibit power-law approach to “equilibrium” values. I will close by discussing experiments and other recent developments in exploring ergodicty and its breakdown in quantum many-body systems. -
10:30
Pause Café
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11:00
François Huveneers, Paris-Dauphine
Many-body localization: What can mathematicians expect to prove?
Abstract: Many-body localization (MBL) is an exciting field that emerged in the mid 2000s. MBL was initially understood as the generalization of Anderson localization to systems where interactions among the quantum degrees of freedom are properly taken into account. It has now been realized that MBL actually provides the best (only?) example of robust ergodicity breaking, i.e. ergodicity breaking for non-integrable systems. In striking contrast to Anderson localization, there is basically no mathematically rigorous result on MBL so far. In this talk, I will critically go through some claims from the physics literature and try to distinguish what could reasonably lead to mathematical theorems. This approach will eventually reveal some interesting features of the MBL physics, in particular of the transition, and we will see that MBL is very different from Anderson localization in many respects. -
12:00
Lunch