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Physical review. B, Condensed matter

Fluctuation properties of thermal solitons

Nikos Theodorakopoulos, Erich W. Weller

Published Apr 15, 1988• 5 citations
Publisher

Abstract

The thermodynamic properties of soliton-bearing systems can be obtained from the statistics of their soliton components, which reflect restrictions on phase space due to interactions. Going beyond the established agreement of the free energy with transfer-integral results, we have successfully tested first derivatives (energy, number density) and second derivatives (specific heat, compressibility) for a one-component soliton gas (corresponding to the case of the low-temperature sine-Gordon chain). A complete description of the equilibrium statistical properties of the soliton gas is given in terms of the averages of occupation numbers and their fluctuations. The latter are characterized by the absence of off-diagonal correlations.

DOI
10.1103/physrevb.37.6200

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The thermodynamic properties of soliton-bearing systems can be obtained from the statistics of their soliton components, which reflect restrictions on phase space due to interactions. Going beyond the established agreement of the free energy with transfer-integral results, we have successfully tested first derivatives (energy, number density) and second derivatives (specific heat, compressibility) for a one-component soliton gas (corresponding to the case of the low-temperature sine-Gordon chain). A complete description of the equilibrium statistical properties of the soliton gas is given in terms of the averages of occupation numbers and their fluctuations. The latter are characterized by the absence of off-diagonal correlations.
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Quantum statistical mechanics of soliton systems is developed in the path integral formalizm by making use of the non-canonical collective coordinate method. The free energy is calculated in the ideal-gas approximation up to the order of two-loop. Explicit calculations are given for the sine-Gordon model. The classical limit of the present quantum calculation agrees with the exact result of the low-temperature expansion of the transfer-integral method. Numerical calculation reveals the quantum effect on the specific heat.
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.
Thermodynamics of the Boltzmann gas consisting of solitons, antisolitons, and breathers of the classical sine-Gordon system is studied by taking their interactions into account. A compact expression for the thermodynamic potential is obtained, which agrees with that obtained from the classical limit of the Bethe-ansatz formulation of the quantum sine-Gordon thermodynamics. We further find that the average number of breathers excited at low temperatures (m\ensuremath{\ll}T\ensuremath{\ll}M, where m and M are the phonon and the soliton masses, respectively) is half the total number of degrees of freedom of the system.