Hal Tasaki's online lectures

Since May 7, 2020 / Online lectures in Japanese
Hal Tasaki's main web page / Hal Tasaki's YouTube channel

Webinar "Variations on a Theme by Lieb, Schultz, and Mattis: Unique Gapped Ground States, Symmetry-Protected Topological Phases, Edge States, Spin Pumping, and all that in Quantum Spin Chains" (August, 2022)

This webinar is based on my presentation at the recent (on-site) conference "Advances in Mathematical Physics: A Conference in Honor of Elliott H. Lieb on his 90th Birthday". I show that various nontrivial "topological" properties of quantum spin chains can be proved in an elementary and intuitive manner by properly using the twist operator of Lieb, Schultz, and Mattis.

Webinar "The Best Answer to the Puzzle of Gibbs about N!! : A short webinar on the work of Sasa, Hiura, Nakagawa, and Yoshida" (June, 2022)

This is a brief commentary on the recent interesting paper by Shin-ichi Sasa, Ken Hiura, Naoko Nakagawa, and Akira Yoshida entitled "Quasi-static decomposition and the Gibbs factorial in small thermodynamic system (link to arXiv)" about the famous N! factor that appears in classical statistical mechanics of identical particles.

Webinar "The Asymmetric Valence-Bond-Solid States in Quantum Spin Chains: The Difference Between Odd and Even Spins" (May, 2022)

A webinar on the recent work by Daisuke Maekawa and Hal Tasaki on SPT phases of quantum spin chains. This is not a heavy lecture. It starts from background, contains few equations and many diagrams.

Online lecture "Rigorous Index Theory for One-Dimensional Interacting Topological Insulators: with a pedagogical introduction to the topological phase transition in the SSH model" (November, 2021)

A lecture based on my recent index theory for one-dimensional topological insulators. Also contains introductory material on the SSH model, which may be useful to non-experts.

Webinar "Rigorous Index Theory for One-Dimensional Interacting Topological Insulators: a brief introduction" (November, 2021)

A short lecture based on my recent index theory for one-dimensional topological insulators.

Online lecture "Symmetry-protected topological (SPT) phases and topological indices in quantum spin chains" (August, 2021)

Almost self-contained two-part (+ appendix) lecture on SPT phases in quantum spin chains. I start from the historical works of Bethe and Haldane, proceed to modern developments, and finally discuss most recent mathematically rigorous results.

Prerequisites: Part 1 Basics of quantum spin systems, Part 2 Some mathematics (group, representation of a group, equivalence class), Appendix: some more math or curiosity

Webinar "Off-Diagonal Long-Range Order Implies Vanishing Charge Gap" (May, 2021)

A short lecture based on the recent work by Hal Tasaki and Haruki Watanabe on simple but fundamental inequality between the charge gap and the (off-diagonal) long-range order in quantum many-body systems with U(1) symmetry.

Webinar "Mott insulator-like BEC in a Tight-Binding System of Interacting Bosons with a Flat Band" (May, 2021)

A short lecture based on the recent work by Hosho Katsura, Naoki Kawashima, Satoshi Morita, Akinori Tanaka, and Hal Tasaki on a new class of exactly solvable models of interacting bosons.

Webinar "Ogata Index for Quantum Spin Chains and Its Applications" (December, 2020)

This is a slightly improved version of my talk in a workshop, where I focused on basic aspects of the Ogata index for quantum spin chains, and discussed applications to problems in physics. The lecture is therefore more mathematical, but probably good for experts. If you are interested in SPT (symmetry protected topological phase) I recommend the new lecture "Symmetry-protected topological (SPT) phases and topological indices in quantum spin chains", which is introductory and also contains strictly more than this one. If you are interested in the Lieb-Schultz-Mattis type theorems only, then I recommend two previous lectures, "Topological index and general Lieb-Schultz-Mattis theorems for quantum spin chains" and/or "Lieb-Schultz-Mattis theorem and its variations for quantum spin chains".

Webinar "Entropy and "thermodynamic" relations for nonequilibrium steady states / Two "twists" in steady state thermodynamics" (November, 2020)

A seminar-style talk based on slightly older work by Teruhisa Komatsu, Naoko Nakagawa, Shin-ichi Sasa, and Hal Tasaki on the construction of thermodynamics for nonequilibrium steady states

Webinar "Hohenberg-Mermin-Wagner type theorems for equilibrium models of flocking" (August, 2020)

A brief introduction to my new work on equilibrium models that mimic active matters. I prove two dimensional equilibrium models in a large class do not exhibit phase transitions.

Webinar "Topological index and general Lieb-Schultz-Mattis theorems for quantum spin chains" (July, 2020)

Recording of my talk given at IAMP One World Mathematical Physics Seminar about recent extension of Lieb-Schultz-Mattis theorems to spin chains with only discrete symmetry.

Online lecture "Efficient heat engines are powerless: a fundamental tradeoff relation in thermodynamics proved in 2016" (May, 2020)

Two-part lecture on the fundamental tradeoff relation between the power and efficiency of a heat engine proved by Naoto Shiraishi, Keiji Saito, and Hal Tasaki. Part 1 is for general audiences, and Part 2 for experts.

Prerequisites: Part 1 Some ideas about college thermodynamics, Part 2 some knowledges about statistical mechanics and stochastic processes

Online lecture "Lieb-Schultz-Mattis theorem and its variations for quantum spin chains" (May, 2020)

Introductory lecture on the Lieb-Schultz-Mattis theorem. I start by reviewing the basic idea of the original proof, and then discuss recent extensions. The same topic is treated in other lectures. This is my first lecture video in English.