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Progress of Theoretical Physics

Dynamical Properties of the One-Dimensional Quantum Sine-Gordon System (g2=4 )

H. Yamamoto, A. D. S. Nagi

Published May 1, 1984• 1 citation
Publisher

Abstract

The dynamical correlation functions for the 1-D quantum sine-Gordon system with g2=4π are investigated analytically (g2 is the quantum parameter). Following a microscopic approach using the fermibose relation, general expressions valid at all temperatures are derived. The high and low temperature limits of the correlation functions are given explicitly.

DOI
10.1143/ptp.71.1100

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The dynamical correlation functions for the 1-D quantum sine-Gordon system with g2=4π are investigated analytically (g2 is the quantum parameter). Following a microscopic approach using the fermibose relation, general expressions valid at all temperatures are derived. The high and low temperature limits of the correlation functions are given explicitly.
The dynamical behavior of the one-dimensional quantum sine-Gordon system with a misfit parameter is investigated at a particular value of the quantum parameter g2=4π. For this purpose the dynamical correlation functions are calculated by using the Fermi-Bose relation. From the behavior of the displacement correlation function we find that the thermal velocity is given by ∼√T/m0 in the commensurate state (m0-| µ 8730|≫T) or in the cross-over region (m0≃| µ \tilde |≫T) and approaches value 1 as T or | µ \tilde | is increased. Here m0 and µ \tilde, respectively, are the gap and the chemical potential in the corresponding fermion system. For the case of denity-density correlation function, we give in the commensurate state expressions which are similar to those derived on the basis of the soliton phenomenology in the classical system. A particular case of the density-density correlation function is discussed in detail by following another route.
With regard to the thermalization problem in isolated quantum systems, we investigate the dynamics following a quantum quench of the sine-Gordon model (sGM) in the Luther–Emery and the semiclassical limits. We consider the quench from the gapped to the gapless phase, as well as the reverse one. By obtaining analytic expressions for the one- and two-point correlation functions of the order parameter operator at zero-temperature, the manifestations of integrability in the absence of thermalization in the sGM are studied. It is shown that correlations in the long-time regime after the quench are well described by a generalized Gibbs ensemble. We also consider the case where the system is initially in contact with a reservoir at finite temperature. The possible relevance of our results to current and future experiments with ultracold atomic systems is also considered.
The sine-Gordon model appears as the low-energy effective field theory of various one-dimensional gapped quantum systems. Here we investigate the dynamics of generic, nonintegrable systems belonging to the sine-Gordon family at finite temperature within the semiclassical approach. Focusing on timescales where the effect of nontrivial quasiparticle scatterings becomes relevant, we obtain universal results for the long-time behavior of dynamical correlation functions. We find that correlation functions of vertex operators behave neither ballistically nor diffusively but follow a stretched exponential decay in time. We also study the full counting statistics of the topological current and find that distribution of the transferred charge is non-Gaussian with its cumulants scaling nonuniformly in time.