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Journal of Physical Studies 23(3), Article 3707 [7 pages] (2019)
DOI: https://doi.org/10.30970/jps.23.3707 LOW-FREQUENCY DYNAMICS OF ONE-DIMENSIONAL SYSTEMS WITH HYDROGEN BONDSR. Ya. Stetsiv
Institute for Condensed Matter Physics National Academy of Sciences of Ukraine, |
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The frequency dependence of the dynamical susceptibility of the dipole-dipole type one-dimensional systems with hydrogen bonds is calculated using the Green's function formalism. The consideration is based on the hard-core boson model. We take into account short-range interactions between protons, and their transfer along hydrogen bonds with the two minima local anharmonic potential as well as their inter-bond hopping. Calculations are performed for a finite one-dimensional cluster with periodic boundary conditions using exact diagonalization technique. The vibrational spectra are studied at $T = 0$ depending on the particles (protons) tunneling frequency on the bond; the influence of the transfer of particles between the bonds on these spectra is also investigated. The density of vibrational states is found, its frequency dependence is analyzed. In the absence of the hopping of particles between bonds, the existence of a mode whose frequency decreases if the tunneling parameter approaches the region of the values that, in the case of a $3d$ system, could correspond to the transition to the ordered (FE) phase, is revealed. But in our 1d case we see, however, the absence of the behavior of the soft mode type. Instead, a new branch appears; its frequency is determined by the energy of repulsion of the protons residing on nearest bonds. An additional complication of the spectrum arises due to the transfer of protons between bonds (in this case the model describes the proton 1d conductor). Another branch appears in this case; its frequency is determined by the energy of interaction of the nearest particles (the case of two protons on hydrogen bond). The splitting of the spectrum can be considered as a manifestation of the appearance of the collective transport of particles along a chain.
PACS number(s): 75.10.Pq, 03.75.Lm, 66.30.Dn