Hydrodynamics, ergodicity, entanglement and localization in interacting lattice models and field theories: September 11 – December 15, 2017

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Organized by: Alexander Abanov, Kristan Jensen, and Vadim Oganesyan

Scientific advisors: Igor Aleiner, David Huse, Anatoli Polkovnikov, Steven Shenker

The program aims to highlight and explore recent progress in understanding the emergence of macroscopic dynamical laws in many-body systems. Traditionally, the challenge of connecting macroscopic and microscopic many-body dynamics was addressed by computing hydrodynamic parameters, e.g. diffusion constants, in some controlled way, e.g. via quantum kinetic formalism, or from properties of low energy renormalized quasiparticles, e.g. in Landau-Fermi or Luttinger liquids. The past decade has brought a considerable broadening of the scope of the inquiry but also sharpening of various important notions. There are now several fast moving and in many cases non-overlapping communities pursuing similar goals, from atomic and condensed matter physics, to high energy and mathematical physics, and this program will provide an opportunity for active participants to meet. Recent developments in hydrodynamics, quantum chaos and localization featuring rigorous results might be of interest to the local math community as well.

Associated workshops:

There will be two one-week workshops associated with the program. The first workshop is on the program’s topics with the focus on outlining the field of research and using the presence of experts representing different fields “Progress in quantum collective phenomena – from MBL to black holes“. The second workshop “Wonders of broken integrability” will be organized by Fabian Essler, Giuseppe Mussardo and Alexei Tsvelik. The latter workshop will focus on the use of methods in the theory of integrable systems to study nearly integrable systems out of equilibrium.

Program themes:

Thermalization vs. equilibration vs localization in lattice models:

The demonstration of the validity of the “eigenstate thermalization hypothesis” in certain strongly interacting quantum lattices paved the way of using it as a tool in detailed explorations of thermalization in many diverse problems. Similarly, the availability of short time experimental data in well controlled cold-atoms experiments motivated the explosion of theoretical activity on so called “quantum quenches”, with concomitant elucidation of entanglement spread and renewed interest in statistical mechanics of integrable systems in low dimensional cases which appear to equilibrate to generalized Gibbs ensembles. Essentially simultaneously, theoretical proposals for the existence of entire phases of interacting matter violating ergodicity were made and confirmed rigorously recently. This field, currently known as many-body localization, has seen explosive growth in the last couple of years, producing several clear counter-examples to accumulated wisdom in thermalized systems, starting with vanishing diffusion constants to power-law relaxation laws to matrix-product-like structure of all eigenstates, and more. Many-body localization also allows for richer variety of spontaneous symmetry breaking than conventional thermalizing systems. There are many outstanding questions and speculations revolving around both details of these phenomena but also dynamical transitions and possibly new intermediate phases connecting.

Nonequilibrium black holes and QFT:

There has also been an a surge of activity devoted to thermalization in the high energy and string theory communities. Much of this work has been devoted to the study of non-equilibrium phenomena in field theories with a gravity dual via the AdS/CFT correspondence. There continues to be a steady flux of numerical results computing transport and evolution in the far-from-equilibrium states dual to black hole formation, in addition to a number of newer threads. These include the study of quantum chaos through Lyapunov exponents, the “butterfly velocity,’’ and fundamental bounds on the growth of chaos which are saturated by theories with an Einstein dual, as well as on the spread of entanglement and its relation to spacetime geometry. In parallel there have been significant advances for transport, including the construction of topological sigma models for dissipative hydrodynamics via the Schwinger-Keldysh formalism, which among other things pin down a systematic formalism for non-linear noise in interacting QFT, to certain robust bounds on transport in disordered theories with a gravity dual.