作用素環セミナー

過去の記録 ~07/23次回の予定今後の予定 07/24~

開催情報 水曜日 16:30~18:00 数理科学研究科棟(駒場) 122号室
担当者 河東 泰之
セミナーURL https://www.ms.u-tokyo.ac.jp/~yasuyuki/tokyo-seminar.htm

2011年11月22日(火)

16:30-18:00   数理科学研究科棟(駒場) 126号室

Spyridon Michalakis 氏
( Institute for Quantum Information and Matter (Caltech))
Stability of topological phases of matter (ENGLISH)
[ 講演概要 ]
The first lecture will be an introduction to quantum mechanics and a proof of Lieb-Robinson bounds for constant range interaction Hamiltonians. The second lecture will build on the first to prove a powerful lemma on the transformation of the interactions of generic gapped Hamiltonians to a new set of rapidly-decaying interactions that commute with the groundstate subspace. I call this "The Energy Filtering Lemma". Then, the third lecture will be on the construction of the Spectral Flow unitary (Quasi-adiabatic evolution) and its properties; in particular, the perfect simulation of the evolution of the groundstate subspace within a gapped path. I will end with a presentation of the recent result on the stability of the spectral gap for frustration-free Hamiltonians, highlighting how the previous three lectures fit into the proof.