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Journal of Physics C Solid State Physics

Commensurate-incommensurate crossover in quantum sine-Gordon model

Kazuo Hida, Masatoshi Imada, M. Ishikawa

Published Sep 10, 1983• 15 citations
Publisher

Abstract

The thermodynamics of the quantum sine-Gordon model with finite winding numbers is investigated by the Bethe ansatz method. The temperature dependences of the specific heat and the winding number are calculated. The crossover from the case with the commensurate ground state to that with the incommensurate ground state is discussed. The quantum effect is shown to be significant in the thermodynamic properties of the system.

DOI
10.1088/0022-3719/16/25/004

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The thermodynamics of the quantum sine-Gordon model with finite winding numbers is investigated by the Bethe ansatz method. The temperature dependences of the specific heat and the winding number are calculated. The crossover from the case with the commensurate ground state to that with the incommensurate ground state is discussed. The quantum effect is shown to be significant in the thermodynamic properties of the system.
Recently Haldane has derived the Bethe ansatz equations describing the ground state properties of the massive Thirring model with finite `hole' density (the quantum sine-Gordon model with finite soliton density). His derivation is explicitly confirmed here using a particular cutoff scheme, and his solutions of the equations in various limits are reviewed with complementary results. The commensurate-incommensurate transition in the two-dimensional sine-Gordon model with a uniaxial misfit is examined at finite temperatures using the results obtained in the massive Thirring model.
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The Bethe-ansatz equations for the thermodynamic properties of the quantum sine-Gordon systems are derived in the zero-charge-sector attractive case. For rational values of the coupling parameter $\frac{\ensuremath{\mu}}{\ensuremath{\pi}}$ these reduce to a finite set, solved here numerically for $\ensuremath{\mu}=[\frac{(n\ensuremath{-}1)}{n}]\ensuremath{\pi}$, for several values of nnn, to give the specific heat as a function of temperature. The "soliton" contribution peaks at $\ensuremath{\simeq}0.4$ soliton masses for $\ensuremath{\mu}=\frac{4}{5}\ensuremath{\pi}$, shifting downward for higher $\ensuremath{\mu}$. A detailed analysis of the sine-Gordon limit of the XYZ\mathrm{XYZ}XYZ spin chain is presented, and a non-Lorentz-invariant feature of that limit is noted.
The commensurate-incommensurate (C-IC) phase transition in the one dimensional quantum sineGordon model at zero temperature is exactly solved with the use of the Bethe ansatz technique for the lattice massive Thirring model. The energy difference between C and IC phases is derived based on the same ground state which is valid in the whole parameter region. It is due to the fact that there is no change in the ground state of the lattice massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model even in the strongly repulsive region in contrast to the continuum massive Thirring model. It is proved in the whole parameter region that the IC phase can be realized with the soliton density proportional to x f E s (Es: formation energy of soliton), when Es becomes negative.