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Nonlinear Response of Kitaev Quantum Spin Liquid

Negahdari, Mohammad Kazem | 2024

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 57573 (04)
  4. University: Sharif University of Technology
  5. Department: Physics
  6. Advisor(s): Langari, Abdollah
  7. Abstract:
  8. Quantum spin liquid (QSL) is an exotic phase of some frustrated magnetic Mott insulators. In this phase, competing interactions result in strong quantum fluctuations which prevent the formation of long-range order even at absolute zero temperature. However, QSL is not solely defined by the absence of order. In the modern definition, it is characterized by fractionalized excitations and emergent gauge fields. The signature of fractional excitations is evident in the form of a broad continuum in conventional probes. However, the continuum spectrum in QSL candidate materials does not definitively indicate whether the continuum is due to fractional excitations or usual ones. Recent theoretical investigations reveals that this broad spectrum is resolved by two-dimensional coherent spectroscopy (2DCS). Using this probe, it is possible to measure non-linear magnetic susceptibilities. The motivation of this thesis is to explore the potential of 2DCS to clearly identify fractional excitations as a defining property of the QSL state of matter. We began our study by examining how non-abelian anyons in the Kitaev honeycomb lattice model, under a weak magnetic field, manifest in 2DCS. By numerically calculating the 2DCS response within the single-matter excitation approximation, we observe distinct signatures of non-abelian anyons. These signals originate from configurations of four-adjacent, two-nonadjacent, and four-far-separated fluxes, each of which is separately detected by this probe. These new signatures are not visible in linear response probes. Furthermore, within moderate regions of the abelian phase, streak patterns appear in the spectrum, which are hallmarks of itinerant Majorana fermions. However, deeper in this phase, the signals sharpen, taking the form of sharp spots. Additionally, we investigated the Kekulé-Kitaev (KK) model, a variant of the Kitaev model with an exact solution. Our ultimate aim was to investigate the 2DCS. However, initially, it was necessary to evaluate the validity of the single-matter approximation, which greatly simplifies our calculations. We demonstrated that this approximation holds for the KK model. Using it, we calculated the dynamical spin structure factor as a linear response and the 2DCS as a nonlinear response. We observed that the linear and nonlinear responses of the original Kitaev and KK models are nearly identical. However, under weak uniform and staggered magnetic fields, these models differ in behavior: the KK model does not support a non-abelian phase under a uniform magnetic field, while it does under a staggered magnetic field. This non-abelian phase could be physically realized by proximity to an antiferromagnetic material, which can induce the staggered magnetic field. In the 2DCS of this non-abelian phase, two non-adjacent fluxes generate stronger signals than other flux configurations. Notably, the model features two degenerate gapless Dirac cones at isotropic couplings. We also examined the stability of these gapless points and demonstrated that the ground state of the Kekulé-Kitaev model, through a unitary transformation, maps to an excited state of the Kitaev model with a uniform flux configuration
  9. Keywords:
  10. Kitaev Model ; Nonlinear Response ; Quantum Spin Liquid ; Two-Dimensional Coherent Spectroscopy ; Fractional Excitations

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