THESIS
2015
ix, 114 pages : illustrations (some color) ; 30 cm
Abstract
We develop a mean-field theory of the 1D spin-1 antiferromagnetic Heisenberg model,
using a two-orbital fermionic representation for the spin-1 operators. Two ansatz with different
orbital pairing symmetries are discussed and the projected mean-field ground states with their
corresponding parent Hamiltonians have also been obtained. Then we study the U(1) spin liquid
state with large spinon Fermi surfaces. The physical conductivity obtained through Ioffe-Larkin
composition rule can support surface plasmon modes propagating along the interface between
the spin liquid and a linear medium, which can be excited using a Kretschmann-Raether
configuration. Next we generalize the linear current response to including nonlinear effects
under the perturbation of a time dependent but spatia...[
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We develop a mean-field theory of the 1D spin-1 antiferromagnetic Heisenberg model,
using a two-orbital fermionic representation for the spin-1 operators. Two ansatz with different
orbital pairing symmetries are discussed and the projected mean-field ground states with their
corresponding parent Hamiltonians have also been obtained. Then we study the U(1) spin liquid
state with large spinon Fermi surfaces. The physical conductivity obtained through Ioffe-Larkin
composition rule can support surface plasmon modes propagating along the interface between
the spin liquid and a linear medium, which can be excited using a Kretschmann-Raether
configuration. Next we generalize the linear current response to including nonlinear effects
under the perturbation of a time dependent but spatially uniform electric field in the framework
of an effective U(1) gauge theory derived through a Fermi-liquid-like approach. The nonlinear
susceptibility can support waves with triple frequency inside the spin liquids through the
process of third harmonic generation. As a byproduct during the Fermi-liquid approach, we
generalize the standard Landau Fermi liquid theory to describe the intrinsic anomalous Hall
conductivity, based on some general symmetric considerations. Fitting result of the anomalous
Hall conductivity is well consistent with the experimental data, and behaves better in lower
frequency range than the simple two-band model.
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