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Physical review. B, Condensed matter

Variational Gaussian wave functional and the (1+1)-dimensional sine-Gordon model

Yumei Zhang, Bo-Wei Xu, Wen-Fa Lu

Published Jan 1, 1994• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.49.854

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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.
A new procedure of trial variational wave functional is proposed for investigating the mass renormalization and the local structure of the ground state of a one-dimensional quantum sine-Gordon model with linear spatial modulation, whose ground state differs from that without modulation. The phase diagram obtained in parameters plane shows that the vertical part of the boundary between soliton lattice phase and incommensurate (IC) phase with vanishing gap sticks at , the IC phase can only appear for and the IC phase regime is enlarged with increasing spatial modulation in the case of definite parameter . The transition is of the continuous type on the vertical part of the boundary, while it is of the first order on the boundary for .