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Theoretical and Mathematical Physics

Diagonalization of bilinear bose Hamiltonians and asymptotic behavior of the Heisenberg fields they generate

L. A. Dadashev, V. Yu. Kuliev

Published Jun 1, 1979• 1 citation
Publisher
DOI
10.1007/bf01017996

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The incipient quantum phase transitions of relevance to nonzero fluctuations and entanglement in Heisenberg clusters are studied in this paper by exploiting negativity as a measure in bipartite and frustrated spin-1 anisotropic Heisenberg clusters with bilinear–biquadratic exchange, single-ion anisotropy and magnetic field. Using the exact diagonalization technique, it is shown that quantum critical points signaled by qualitative changes in behavior of magnetization and particle number are ultimately related to microscopic entanglement and collective excitations. The plateaus and peaks in spin and particle susceptibilities define the conditions for a high/low-density quantum entanglement and various ordered phases with different spin (particle) concentrations.
We study the phase diagram of the spin-1 quantum bilinear-biquadratic antiferromagnet on the kagome lattice using exact diagonalization and the density matrix renormalization group algorithm. The SU(3)\mathrm{SU}(3)SU(3)-symmetric point of this model Hamiltonian is a spontaneously trimerized state whose qualitative nature persists even at the Heisenberg point, a finding that contrasts previous proposals. We report the ground state energy per site of the Heisenberg model to be $\ensuremath{-}1.410(2)$ and establish the presence of a spin gap.