Lecture 1: Topology of electronic materials and their linear and nonlinear responses
Date and time: 26 November, 16:00 hrs
Certain natural geometric properties of electron wavefunctions in a crystal turn out to explain a vast range of experimentally relevant properties. The original example was the explanation of the integer quantum Hall effect by Thouless and co-workers in terms of the “Berry curvature” derived from Bloch states. We now understand that a kind of gauge field in the Brillouin zone is the key to many equilibrium and linear-response properties, and current work is seeking to generalize these results to nonlinear and non-equilibrium properties as well. This talk reviews the basic concepts of wavefunction geometry starting from basic notions of undergraduate quantum mechanics, then covers more recent applications to new topological states, with a particular focus on effects beyond the standard adiabatic limit.
Lecture 2: The fates of pure many-particle systems: some hydrodynamical limits of spins and qubits
Date and time: 27 November, 14:00 hrs
One of the first nontrivial examples of quantum matter to be understood at equilibrium was the behavior of a chain of two-state spins, or qubits, entangled by nearest-neighbor interactions. Hans Bethe’s solution of the ground state in 1931 eventually led to the concept of Yang-Baxter integrability, and the thermodynamics were fully understood in the 1970s. However, the dynamical properties of this spin chain at any nonzero temperature remained perplexing until some unexpected theoretical and experimental progress beginning around 2019. Atomic emulators and quantum computers are beginning to complement solid-state quantum magnetism experiments, and computer scientists, physicists, and mathematicians all have their own reasons to care about the dynamics of simple arrangements of quantum spins. The last part of the talk covers how dynamics of more complicated spin models in higher dimensions are being used to search for emergent gauge fields and other phenomena.
Lecture 3: Quantum information and other tools for understanding dynamical regimes far from thermalization
Date and time: 28 November, 14:00 hrs
Many-body localization is one of several conceptual example of how an interacting system of many particles can fail to reach thermal equilibrium. This talk discusses the emerging understanding of systems that fail to thermalize, with a particular focus on quantum information quantities such as entanglement. The importance of entanglement as a constraint on classical computation is complemented by new approaches to measure entanglement in solid-state systems using old techniques such as neutron scattering. New experimental systems in quantum matter such as nitrogen vacancy centers in diamond are, at least on accessible time scales, neither localized nor conventionally thermalizing, and while simple phenomenological models seem to capture the physics in some cases, the reasons why such models work are so far not well understood.
About the speaker: Joel Moore is Chern-Simons Professor of Physics at the University of California, Berkeley, and a Senior Faculty Scientist at Lawrence Berkeley National Laboratory. His work in theoretical physics studies quantum matter with a focus on the remarkable phenomena that emerge as consequences of entanglement and topology. He received his A.B. in physics from Princeton in 1995 and spent a Fulbright year at TIFR before graduate studies at MIT. He then was a postdoc at Bell Labs before joining the Berkeley faculty in 2002. He is an elected member of the National Academy of Sciences (2022), a Simons Investigator (2013-2023), and a Fellow of the American Physical Society (2013). He previously served as member and chair of the advisory board of the Kavli Institute for Theoretical Physics.
This lecture series is part of the discussion meeting "Quantum Many-Body Physics in the Age of Quantum Information".