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Springer proceedings in physics

Excitations and Critical Behavior in Generalized Heisenberg Spin Chains

J. C. Bonner, Gerhard H. Muller, John B. Parkinson

Published Jan 1, 1987• 0 citations
Publisher
DOI
10.1007/978-3-642-73107-5_19

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We investigate the properties of a generalized Rabi model by replacing the two-level atom in Rabi model with a ferromagnetic Heisenberg spin chain. We find that the dynamical behavior of the system can be divided into four categories. The energy spectrum of the ground state and some low excited states are obtained. When the magnons and the photon are in resonance, the model is exactly solvable and the rigorous solution is obtained. Near the resonance point where the detuning is small, the system is studied with the help of perturbation theory. This model has a spontaneously breaking of parity symmetry, suggesting the existence of a quantum phase transition. The critical exponent from the normal phase is computed.
We study the infinite-temperature properties of an infinite sequence of random quantum spin chains using a real-space renormalization group approach, and demonstrate that they exhibit nonergodic behavior at strong disorder. The analysis is conveniently implemented in terms of SU(2)_{k} anyon chains that include the Ising and Potts chains as notable examples. Highly excited eigenstates of these systems exhibit properties usually associated with quantum critical ground states, leading us to dub them "quantum critical glasses." We argue that random-bond Heisenberg chains self-thermalize and that the excited-state entanglement crosses over from volume-law to logarithmic scaling at a length scale that diverges in the Heisenberg limit k→∞. The excited state fixed points are generically distinct from their ground state counterparts, and represent novel nonequilibrium critical phases of matter.
We consider in detail the ground-state properties of recently introduced generalized Heisenberg models which can have several spin operators at each site and which interpolate smoothly between Heisenberg chains of different spin lengths. We show that the mappings to field-theoretical models used to describe the critical properties of the Heisenberg model remain valid in the composite-spin model. In models which interpolate between the spin-(1/2 and the spin-1 behavior, these mappings predict an extended singlet phase around the isotropic antiferromagnetic point whenever the models move away from the spin-(1/2 point. Numerical calculations on finite chains seem to confirm the existence of this singlet phase. The phase boundaries are, however, found to be independent of the interpolation parameter, and thus in disagreement with the predictions of the continuum theory, indicating its limitation.