Explore a 41-minute lecture on a Lieb-Schultz-Mattis type theorem without continuous symmetry, presented by Hal Tasaki at the International Centre for Theoretical Sciences. Delve into the intricacies of quantum spin chains, matrix product states, and operator algebraic approaches in quantum systems with infinite degrees of freedom. Learn about the original theorem's proof, typical theorems, and their implications. Examine the group Z2 * Z2, its representations, and transformations of single spins. Follow the progression from specific theorems to more general ones, including extensions to symmetry and state. Gain insights from a mathematical physicist's perspective on operator algebraic approaches to spin systems. Conclude with a summary and Q&A session to solidify understanding of this advanced topic in theoretical physics.
A Lieb-Schultz-Mattis Type Theorem Without Continuous Symmetry by Hal Tasaki
International Centre for Theoretical Sciences via YouTube
Overview
Syllabus
A Lieb-Schultz-Mattis type theorem without continuous symmetry
Lieb-Schultz-Mattis type theorem in quantum spin chains without continuous symmetry a "no non-degenerate scar theorem"
Lieb-Schultz-Mattis LSM type theorem
Proof of the original theorem
A Typical Theorem
Remarks on the Theorem 1
Remarks on the Theorem 2
Remarks on the Theorem 3
Remarks on the Theorem 4
The group Z2 * Z2 its representation and projective representation
Z2 X Z2 transformation of a single spin
Theorem for Matrix Product States MPS
Matrix Product States MPS
Theorem for MPS
Proof of Theorem 1'
Toward the Full Theorem
From Theorem 1' to Theorem 1
About operator algebraic approaches in quantum systems with infinite degrees of freedom
Opinions of a mathematical physicist on operator algebraic approaches to spin systems student
Outline of the Proof
Algebras for the half-infinite chain
New Hilbert space H
The Cuntz algebra
The core of the proof
Extensions
Symmetry
State
General Theorem
Summary
Q&A
Taught by
International Centre for Theoretical Sciences
