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Progress of Theoretical Physics

Soliton Lattices at Finite Temperatures

Ken'ichi Takano

Published Jun 1, 1984• 3 citations
Publisher

Abstract

In one-dimensional fermion-boson coupled systems which belong to a certain class together with the Takayama-Lin-Liu-Maki model, soliton lattices change their soliton densities with increasing temperature when the fermion numbers are fixed. The temperature dependences are classified into two types depending upon their soliton formation energies.

DOI
10.1143/ptp.71.1401

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In one-dimensional fermion-boson coupled systems which belong to a certain class together with the Takayama-Lin-Liu-Maki model, soliton lattices change their soliton densities with increasing temperature when the fermion numbers are fixed. The temperature dependences are classified into two types depending upon their soliton formation energies.
The effect of quantum lattice fluctuations on the dimerized ground state is studied in the half-filled-band Takayama-Lin-Liu-Maki model. The nonadiabatic effect due to finite phonon frequency ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$\ensuremath{\gtrsim}0 is treated through an energy-dependent electron-phonon scattering function \ensuremath{\delta}(${\mathit{k}}^{\ensuremath{'}}$,k) introduced by means of a unitary transformation. This leads to a weakening of the effective (adiabatic) potential stabilizing the dimerized state and results in four-fermion interaction. By decoupling of the electronic correlations we show that our approach gives a good description of the continuous variation of the dimerization as functions of the dimensionless coupling constant g2{\mathit{g}}^{2}g2 and the phonon frequency ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$ when the ratio ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$/\ensuremath{\pi}t (t is the electron hopping integral) is not large. Our results show that, at least in the weak-coupling limit, quantum lattice fluctuations change the functional dependence of the dimerization parameter mp{\mathit{m}}_{\mathit{p}}mp​ on the coupling constant even if the ratio ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$/\ensuremath{\pi}t is small (but finite). In the spin-1/2 case our result is the same as that predicted by Fradkin and Hirsch. But in the spinless case we still predict a long-range dimerization order even if the coupling is weak and ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$/\ensuremath{\pi}t is finite. In the large ${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$ (antiadiabatic) limit we show that our effective Hamiltonian becomes an n-component Gross-Neveu model and the ratio mp{\mathit{m}}_{\mathit{p}}mp​(${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$=\ensuremath{\infty})/mp{\mathit{m}}_{\mathit{p}}mp​(${\mathrm{\ensuremath{\omega}}}_{2{\mathit{k}}_{\mathit{F}}}$=0) is equal to 1/cosh(\ensuremath{\pi}/2ng2{\mathit{ng}}^{2}ng2) (n=1: spinless; n=2: spin-1/2). By using the same input parameters as those of some previous authors we get a 7.2% reduction of the dimerization parameter mp{\mathit{m}}_{\mathit{p}}mp​ compared with the adiabatic value. \textcopyright{} 1996 The American Physical Society.
The thermal renormalization of the Bethe-ansatz excitation spectrum for the sine-Gordon system is presented. For the soliton mass, the results agree closely with those of Maki and Takayama over a significant temperature range, but the sudden decrease in mass they predict near a particular temperature is not found. For the Bethe-ansatz excitation corresponding to the phonon at zero temperature, the rest mass changes rapidly as the temperature increases, even near the classical limit. This suggests that at finite temperature this excitation (the one-string) no longer corresponds to the physical phonon.