作用素環セミナー
過去の記録 ~02/12|次回の予定|今後の予定 02/13~
開催情報 | 水曜日 16:30~18:00 数理科学研究科棟(駒場) 122号室 |
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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)
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.
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.