[F] Seminar at M. Ueda Group, Univ. Tokyo, JAPAN, Jan 24 (2013)

PM1:00, Rm. 933, buld. 9, Univ. Tokyo

Title:Symmetry and order parameters for topological phases

Abstract:

Beyond the great success of the Ginzburg-Landau theory associated with symmetry breaking (SB), condensed matter physicists focus on more than that recently. That is, phases without any fundamental SB but possessing characteristic feature are of the central interest, which are the quantum/spin liquids. This class of matter includes quite wide varieties such as quantum (spin) Hall states, gapped quantum spins, anisotropic superfluids/superconductors and graphene. Some of cold atoms and photonic systems belong to the class as well.

Even though the SB is absent, too much generic states are boring. Then still the symmetry plays an important role to constrain the physical states. Gauge symmetries, time-reversal and charge conjugation are important examples. When the quantum/spin liquid is stable against for some perturbation due to geometrical constraints, one may consider the state topological.

As for the topological phases with some symmetry protection, we can define "topological order parameter" using topological objects, such as gap nodes, quantized Berry phases and Chern numbers. Some of edge states, which are induced by geometric perturbation such as boundaries and impurities, are again topologically stable and used for the topological order parameters. This is the bulk-edge correspondence. As for the gapped cases, these topological order parameters are adiabatic invariants and useful for identification of the quantum phase transition.

We will describe generic idea of the topological phases and show validity of our topological characterization for various quantum phases.

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[P] MANA seminar & lectures at X. Hu Group at NIMS, Tsukuba, JAPAN, March 6 (2013) |
国際会議、研究会、セミナー |
[P] 2013 EMN West Meeting on Topological Insulators, Houston, USA Jan 7-10(2013 |