Mathematics 277Z

Quantum Spin Systems and Their Ground States (220500)

Daniel Spiegel

2027 Spring (4 Credits)

Schedule: WF 0300 PM - 0415 PM

Instructor Permissions: None

Enrollment Cap: n/a

This course will provide an introduction to the C*-algebraic formalism of quantum spin systems. Comfort with basic functional analysis of Banach and Hilbert spaces will be assumed. The theory of operator algebras will play a significant role and will be introduced as needed, but no prior knowledge of operator algebras is expected. We will cover Lieb-Robinson bounds and some of their many consequences for the ground states of such systems, such as exponential decay of correlations and quasi-adiabatic evolution. Following this, we will focus on entanglement properties and topological properties of ground states and their phases.

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