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Acta Physica Sinica

SINE-GORDON MODEL AND GAUSSIAN WAVE FUNCTIONAL

Xu Bo-wei, Yumei Zhang, Wen-Fa Lu, (1)上海交通大学物理系,上海200030; (2)同济大学物理系,上海200092

Published Jan 1, 1993• 2 citations
Publisher

Abstract

With a general Gaussian wave functional, we study the ground states, one particle states, and two particle states of the sine-Gordon model. At the Coleman's critical point, the sine-Gordon system tends to a system of massless free bosons which possesses conformal symmetry. We also show that there exist bound states in two particle states as long as the renormalized mass remains finite.

DOI
10.7498/aps.42.1573

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With a general Gaussian wave functional, we study the ground states, one particle states, and two particle states of the sine-Gordon model. At the Coleman's critical point, the sine-Gordon system tends to a system of massless free bosons which possesses conformal symmetry. We also show that there exist bound states in two particle states as long as the renormalized mass remains finite.
The (1+1)-dimensional sine-Gordon model is studied in the framework of the variational Gaussian wave functionals. The renormalized mass depends on two dimensionless parameters. In the phase diagram a first-order phase transition will replace the second-order phase transition for large bare mass. The spectrum of the two-particle states consists of a continuum of scattering states and the isolated values connected to the excitonlike bound states. The energy of the bound states and the phase shifts of the scattering states are explicitly calculated.
We have developed a quantum-mechanical approach to study the critical properties of the quantum sine-Gordon equation describing a massless scalar field in 1+1 space-time dimensions with interaction density proportional to cos(${\mathrm{\ensuremath{\beta}}}_{0}$\ensuremath{\varphi}). The main feature of the present theory is to find an appropriate starting point for perturbation expansion, which can directly treat the infrared divergences encountered in the conventional perturbation theory. Exact critical conditions for the phase transition of the model are derived; and the quantum sine-Gordon Hamiltonian is found to correspond exactly to a free-field model. Near the critical regime, a gap will open near zero momentum in the excitation spectrum, and the corresponding ground-state wave function is a pairing quasiparticle state, analogous to the BCS superconducting state. It is proved that this ground state will possess quasi-long-range and quasi-off-diagonal long-range correlations. Comparisons with the Kosterlitz-Thouless classical theory of the two-dimensional Coulomb gas are also made.