[F] MANA seminar & lectures at Prof. X. Hu Group at NIMS, Tsukuba, JAPAN, March 6 (2013)
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MANA Seminar:
Title: "Topological phases and bulk-edge correspondence"
Abstract:
Quantum/spin liquids are states without any fundamental symmetry
breaking. They are featureless as a bulk but some of them possess
characteristic boundary states with edges or impurities. Historical
and typical examples are quantum Hall states and Haldane spin chain.
Quantum spin Hall states as the topological insulators also belong to
it. Many of them are topologically nontrivial and it implies the
existence of edges states and vice versa. This is the bulk-edge
correspondence, which is further applied for variety of quantum states
such as graphene, anisotropic-superconductors, cold atoms and
photonics crystals. We will explain idea of topological phases and the
bulk-edge correspondence supplemented with examples.
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Lectures:
"Characterization of topological phases"
1. Topological phases
1.1 Symmetry breaking and Nambu Goldstone boson
1.2 Quantum/Spin liquids
1.3 Quantum Hall states and adiabatic heuristic argument
1.4 Gapped or gapless
2. Topological order parameters
2.1 Gap nodes
2.2 Adiabatic invariants
2.3 Bulk-edge correspondence
2.4 Entanglement entropy
3. Berry connections
3.1 Chern numbers for the quantum Hall states
3.2 Berry phase and its quantization
3.3 Singlet/Dimer order parameter
4. Characterization for the zoo
4.1 Quantum spin chains and ladders
4.2 BEC-BCS crossover
4.3 Orthogonal dimers
4.4 Frustrated fermions
5. Bulk-edge correspondence
5.1 QHE and zero modes of graphene
5.2 Topological invariant of the edge states
5.3 Exact bulk-edge correspondence
5.3 Bulk-edge correspondence of Dirac fermions
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[P]"Quantum effects in graphene and related material ", Univ. Tsukuba, Tsukuba, March 19 (2013) |
国際会議、研究会、セミナー |
[P] Seminar at M. Ueda Group, Univ. Tokyo, JAPAN, Jan 24 (2013) |