33,325 research outputs found
On the KP Hierarchy, Algebra, and Conformal SL(2,R)/U(1) Model: II. The Quantum Case
This paper is devoted to constructing a quantum version of the famous KP
hierarchy, by deforming its second Hamiltonian structure, namely the nonlinear
algebra. This is achieved by quantizing the conformal
noncompact coset model, in which appears
as a hidden current algebra. For the quantum algebra at
level , we have succeeded in constructing an infinite set of commuting
quantum charges in explicit and closed form. Using them a completely integrable
quantum KP hierarchy is constructed in the Hamiltonian form. A two boson
realization of the quantum currents has played a crucial
role in this exploration.Comment: 33
Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the Z2-invariant in topological insulators
We study the bulk-edge correspondence in topological insulators by taking
Fu-Kane spin pumping model as an example. We show that the Kane-Mele invariant
in this model is Z2 invariant modulo the spectral flow of a single-parameter
family of 1+1-dimensional Dirac operators with a global boundary condition
induced by the Kramers degeneracy of the system. This spectral flow is defined
as an integer which counts the difference between the number of eigenvalues of
the Dirac operator family that flow from negative to non-negative and the
number of eigenvalues that flow from non-negative to negative. Since the bulk
states of the insulator are completely gapped and the ground state is assumed
being no more degenerate except the Kramers, they do not contribute to the
spectral flow and only edge states contribute to. The parity of the number of
the Kramers pairs of gapless edge states is exactly the same as that of the
spectral flow. This reveals the origin of the edge-bulk correspondence, i.e.,
why the edge states can be used to characterize the topological insulators.
Furthermore, the spectral flow is related to the reduced eta-invariant and thus
counts both the discrete ground state degeneracy and the continuous gapless
excitations, which distinguishes the topological insulator from the
conventional band insulator even if the edge states open a gap due to a strong
interaction between edge modes. We emphasize that these results are also valid
even for a weak disordered and/or weak interacting system. The higher spectral
flow to categorize the higher-dimensional topological insulators are expected.Comment: 9 page, accepted for publication in Nucl Phys
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