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Journal of Physical Studies 25(2), Article 2702 [8 pages] (2021)
DOI: https://doi.org/10.30970/jps.25.2702 STATE DIAGRAMS OF ONE-DIMENSIONAL ION CONDUCTORS WITH THE TWO MINIMA LOCAL ANHARMONIC POTENTIAL FOR IONSR. Ya. Stetsiv{1}, O. Ya. Farenyuk{1,2}
1Institute for Condensed Matter Physics NAS of Ukraine,
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We examine one-dimensional ion conductors with the two minima local anharmonic potential for ions using an extended hard-core boson lattice model. Energy spectrum and one-particle spectral densities were calculated using the exact diagonalization method for finite one-dimensional system with periodic boundary conditions. It was shown that at $T = 0$ the repulsive short-range interaction between particles results in the emergence of a gap in the energy spectrum in the limit of half-filling of ionic sites (the emergence of the charge-density-wave phase). A similar effect is also created by the influence of the modulating field. The charge-density-wave (CDW) phase exists only at half-filling of ionic sites. When we walk away from the half-filling, we get in a superfluid (SF) phase. In this phase, conductivity of the system grows by a few orders. The above phases and phase transitions between them for a one-dimensional system exist only at $T = 0$. We confirmed the presence of the SF phase by obtaining a sharp peak (maximum) of the Fourier transform of the real part of commutator Green's function of bosons at $k=0$, $ω = 0$, $T = 0$. We did not obtain a predictable divergence of this static susceptibility in the SF phase, which is predefined by the finite size of the ion conductor and maybe its onedimensionality. However, we showed that at small temperatures it is a few orders smaller than at $T = 0$, and with further increases in temperature the maximum of this susceptibility becomes smeared, which testifies that in a one-dimensional system a SF phase is only at $T = 0$.
We obtained phase diagrams of equilibrium states of the system dependent on the interactions between ions and the modulating field. It is shown that the width of the CDW phase (in $μ$ coordinates) grows with an increase in the value of the modulating field. Dependence of the width of the CDW phase on short-range interactions between ions is more complex. With large values of the interactions and their further increase, we obtained a linear dependence of the CDW phase width on the values of interactions between particles. With intermediate values of the interactions, narrowing of the CDW phase is possible and a minimum of its width is observed (in $μ$ coordinates) depending on the values of interactions between ions. A characteristic feature of all the latter diagrams is that the line separating the SF and Mott insulator (MI) phases is strictly a straight line depending on the values of interactions between ions.
Key words: ion conductor, hard-core boson model, spectral density, state diagrams.