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arXiv:hep-th/0109118

Conformal Gaussian Approximation

Anı́bal Iucci, Carlos Naón

Published Sep 14, 2001• 1 citation
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Abstract

We present an alternative way to determine the unknown parameter associated to a gaussian approximation in a generic two-dimensional model. Instead of the standard variational approach, we propose a procedure based on a quantitative prediction of conformal invariance, valid for systems in the scaling regime, away from criticality. We illustrate our idea by considering, as an example, the sine-Gordon model. Our method gives a good approximation for the soliton mass as function of $β$.

DOI
10.48550/arxiv.hep-th/0109118

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We present an alternative way to determine the unknown parameter associated to a gaussian approximation in a generic two-dimensional model. Instead of the standard variational approach, we propose a procedure based on a quantitative prediction of conformal invariance, valid for systems in the scaling regime, away from criticality. We illustrate our idea by considering, as an example, the sine-Gordon model. Our method gives a good approximation for the soliton mass as function of βββ.
Starting from the Gaussian-variational approximation the state of the single sine-Gordon soliton is constructed using the coupled cluster method. The quantum contributions to the soliton mass and those to the space dependence of the soliton are computed and found to be non-negligible. If the coupling constant ${\ensuremath{\beta}}^{2}$ approaches the critical value $4\ensuremath{\pi}$ the mass becomes classical, but in other respects the soliton remains a quantum object.
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.
Statistical systems near a classical critical point have been intensively studied from both theoretical and experimental points of view. In particular, correlation functions are of relevance in comparing theoretical models with the experimental data of real systems. In order to compute physical quantities near a critical point, one needs to know the model at the critical (conformal) point. In this line, recent progress in the knowledge of conformal field theories, through the conformal bootstrap, gives the hope of getting some interesting results also outside of the critical point. In this paper, we will review and clarify how, starting from the knowledge of the critical correlators, one can calculate in a safe way their behavior outside the critical point. The approach illustrated requires the model to be just scale invariant at the critical point. We will clarify the method by applying it to different kind of perturbations of the 2D Ising model.