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Operator Algebra Seminars
Seminar information archive ～05/01｜Next seminar｜Future seminars 05/02～
| Date, time & place | Wednesday 16:30 - 18:00 122Room #122 (Graduate School of Math. Sci. Bldg.) |
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2011/11/22
16:30-18:00 Room #126 (Graduate School of Math. Sci. Bldg.)
Spyridon Michalakis ( Institute for Quantum Information and Matter (Caltech))
Stability of topological phases of matter (ENGLISH)
Spyridon Michalakis ( Institute for Quantum Information and Matter (Caltech))
Stability of topological phases of matter (ENGLISH)
[ Abstract ]
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.
