In the Winter 2026, I am organizing a working group on the mathematics of quantum spin systems. If you are interested in joining, please contact me by email first to check that you have the prerequisite. I expect a strong background in linear algebra (typically proof-based abilities on problems involving singular values and/or tensor products. Typically Math 318 or 340 with an excellent grade, equivalent classes, or personal experience). If joining, you're expected to give a 1+hour long presentation. Topics to be covered
Interest and availability form
Lunch (vegetarian pizza) is provided during our regular meeting, Thursdays, 12-2PM, MOR 234.
January 8th - 12-2PM in PDL C401 - Alexis Drouot: An introduction to quantum spin systems. Notes
January 22nd - 12-2PM in PDL C401 - Miles Mai: Reduced States and Observables on Subsystems. Notes
January 28th - 3:30-4:30PM in DEN 111 - AGD seminar by Matthew Hastings: Lieb-Robinson bounds and applications to quantum spin systems: how dynamics control statics.
January 29th - 12-2PM in MOR 234 - Shiang-Bin Chiu: Emergent Speed Limits from Locality: Lieb-Robinson Bounds. References (Chapter 3.1, 3.2)
February 5th - 12-2PM in MOR 234 - Yusen Ye: Gapped ground states have exponentially small correlations. References (Chapter 6.1), Notes
I'll talk about the exponential decay of the gapped ground state, where we can convert the temporal bound from the Lieb-Robinson theorem to a spatial bound. We will also talk about the area law of 1D entanglement entropy and Lieb-Schultz-Mattis theorem, which can be used to determine if a system is gapped.
February 12th - 12-2PM in MOR 234 - Alexis Drouot: Hastings' ground state factorization
February 19th - 12-2PM in MOR 234 - Amelie Martin: Classical and quantum entropy
February 19th - 4:30-6PM in PDL C38 - Alexis Drouot: Up, down, and all around: A gentle introduction to quantum spins systems.
February 26th - 12-2PM in MOR 234 - Dante Tjowasi: Gapped ground states that overlap with pure tensors have controlled entropy
March 5th - 12-2PM in MOR 234 - Liam Bonds: The 1D area law: gapped ground states in 1D systems have bounded entropy
March 12th - 12-2PM in MOR 234 - Approximation of 1D gapped ground states by matrix product states