# Dynamics of one-dimensional quantum spin systems with competing interactions at zero temperature

#### Abstract

This dissertation reports three projects on the zero-temperature dynamics of some prominent one-dimensional (1D) quantum spin systems. A common feature of all three model systems is the presence of competing interactions. Each project employs the recursion method in combination with recently developed techniques of continued-fraction analysis.^ The first model investigated is the 1D s = 1 XXZ model with an additional uniaxial single-site term. The results for the in-plane and out-of-plane spin dynamic structure factors $S\sb{\mu\mu}(q,\omega),\ \mu = x,\ z$ are found to bear the characteristic signatures of several phase transitions between the Haldane phase, the Neel phase, the singlet phase, and two different critical phases.^ The second model investigated is the 1D s = 1/2 nearest-neighbor (nn) XXZ model with an additional isotropic next-nearest-neighbor (nnn) coupling. The focus here is on the dynamic structure factors $S\sb{zz}(q,\omega)$ and $S\sb{DD}(q,\omega$), which describe (for q = $\pi$) the fluctuations of the Neel and dimer order parameters, respectively. By means of a weak-coupling continued-fraction analysis, the dependence on the exchange constants of the infrared exponent, the renormalized bandwidth of spinon excitations, and the spectral-weight distributions of S$\sb{zz}(\pi,\omega$) and $S\sb{DD}(\pi,\omega$) in the weak-coupling regime of the spin-fluid phase are calculated. For some parameter values, a discrete branch of excitations above the spinon continuum is found. The discrete states contribute to $S\sb{zz}(q,\omega$) but not to $S\sb{DD}(q,\omega$). A strong-coupling continued-fraction analysis is employed for the study of the dynamically relevant dispersions and spectral-weight distributions of $S\sb{zz}(q,\omega$) and $S\sb{DD}(q,\omega$) in the strong-coupling regime of the spin-fluid phase and in the dimer or Neel ordered phases. Special attention is given to the case where the pure dimer ground state is realized exactly.^ The third model investigated is the 1D s = 1 XXX model with bilinear and biquadratic exchange. Here the study is focused on the special coupling ratio where the valence-bond-solid ground state is realized. The excitation spectra which are dynamically relevant for the dynamic spill and dimer structure factors, $S\sb{zz}(q,\omega$) and $S\sb{DD}(q,\omega$), are investigated via two different types of continued-fraction analysis. The spectral weight in $S\sb{ZZ}(q,\omega$) is found to be carried predominantly by a single branch of quasi-particles and a continuum of two-particle scattering states thereof, whereas the spectral weight in $S\sb{DD}(q,\omega$) is dominated by the continuum alone, which shrinks to a single mode at $q = \pi$. ^

#### Subject Area

Physics, Condensed Matter

#### Recommended Citation

Yongmin Yu, "Dynamics of one-dimensional quantum spin systems with competing interactions at zero temperature" (1996). Dissertations and Master's Theses (Campus Access). Paper AAI9702109.
http://digitalcommons.uri.edu/dissertations/AAI9702109

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