Wojciech De Roeck: Absence of Normal Heat Conduction in Strongly Disordered Interacting Quantum Chains

We prove that in strongly disordered, interacting, quantum chains, the conductance of a chain of length L vanishes faster than 1/L. This means that transport is anomalous in such chains. This phenomenon was first claimed in 2005 and is related to what was later called "Many-body Localization". 

Géraldine Haack: Quantum Kinetic Uncertainty Relations in Mesoscopic Conductors

Kinetic Uncertainty Relations (KURs) establish quantum transport precision limits by linking signal-to-noise ratio(SNR) to the system's dynamical activity, valid in the weak-coupling regime where particle-like transport dominates. At strong coupling, quantum coherence challenges the validity of KURs and questions the meaning of the concept of activity itself.

In this talk, I will introduce a generalized dynamical activity valid at arbitrary coupling and discuss steady-state quantum KUR (QKUR) expressed in terms of this generalized activity. Explicit expressions are obtained within Green's function and Landauer-Büttiker formalisms. This QKUR ensures that uncertainty relations are valid across all coupling strengths, offering a general framework for out-of-equilibrium quantum transport precision analysis.

These concepts will be illustrated with paradigmatic quantum-coherent mesoscopic devices: a single quantum channel pinched by a quantum point contact and open single- and double-quantum dot systems. These result establish a general theoretical framework for quantifying precision limits in open quantum systems far from equilibrium.

Masaki Oshikawa: Symmetry-Protected Topological phases and Duality

Symmetry-Protected Topological (SPT) phases are phases without any conventional local order parameter, but distinct from the trivial phase in the presence of a certain symmetry. The concept was first proposed by Gu and Wen in 2009 as a generalization of topological insulators discovered earlier, However, the prototypical example of the SPT phases, the Haldane gap phase in odd-integer spin chains, was discovered much earlier in the 1980s. Thanks to the pivotal construction of the Affleck-Kennedy-Lieb-Tasaki (AKLT) state, numerous "topological" properties of the Haldane gap phase were identified by the 1990s. In particular, a non-local transformation introduced by Kennedy and Tasaki maps the Haldane gap phase and a conventional Spontaneous Symmetry Breaking (SSB) phase. The duality picture could have naturally led to the concept of the SPT phases.

In this talk, I will review the concept of SPT phases from the duality point of view, and its historical developments. I will also discuss the recent resurgence of the duality approach, with applications including a systematic construction of SPT phases including a novel variety of “gapless SPT phases”.

Sagar Vijay: The emergent statistical mechanics of random quantum many-body dynamics

Random quantum circuits provide a rich set of theoretical models to understand universal properties of quantum many-body evolution. Connections between random circuits and an emergent classical statistical mechanics shed light on a variety of phenomena, including entanglement growth in quantum many-body evolution, phase transitions in far-from-equilibrium quantum dynamics, and new applications to quantum algorithms.