Sine-Gordon Model: Renormalization Group Solution and Applications
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| Natura: | Artículo científico |
| Lingua: | en |
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Sociedade Brasileira de Física
2013
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| _version_ | 1876435102966218752 |
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| author | Mariana Malard |
| author_facet | Mariana Malard |
| contents | Sine-Gordon Model: Renormalization Group Solution and Applications Mariana Malard Física, Astronomía y Matemáticas Sine Kosterlitz ology model Gordon model Hubbard model The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is described, in which the sine-Gordon field is decomposed into slow and fast modes. An effective theory for the slow modes is derived and rescaled to yield the flow equations for the model. The resulting Kosterlitz–Thouless phase diagram is obtained and discussed in detail. The gap in this theory is estimated in terms of the sine-Gordon model parameters. The mapping between the sine-Gordon model and one-dimensional interacting-electron models, such as the gology and Hubbard models, is discussed. On the basis of the results borrowed from previous renormalization-group results for the sine-Gordon model, different aspects of Luttinger liquid systems are described, such as the nature of the excitations and phase transitions. The calculations are thoroughly and pedagogically described, to even reach the reader with no previous experience with the sine-Gordon model or the renormalization group approach. 2013 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46426434008 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.3 Vol.43 |
| format | Artículo científico |
| id | redalyc_46426434008 |
| institution | Redalyc |
| language | en |
| publishDate | 2013 |
| publisher | Sociedade Brasileira de Física |
| spellingShingle | Sine-Gordon Model: Renormalization Group Solution and Applications Mariana Malard Física, Astronomía y Matemáticas Sine Kosterlitz ology model Gordon model Hubbard model Sine-Gordon Model: Renormalization Group Solution and Applications Mariana Malard Física, Astronomía y Matemáticas Sine Kosterlitz ology model Gordon model Hubbard model The sine-Gordon model is discussed and analyzed within the framework of the renormalization group theory. A perturbative renormalization group procedure is described, in which the sine-Gordon field is decomposed into slow and fast modes. An effective theory for the slow modes is derived and rescaled to yield the flow equations for the model. The resulting Kosterlitz–Thouless phase diagram is obtained and discussed in detail. The gap in this theory is estimated in terms of the sine-Gordon model parameters. The mapping between the sine-Gordon model and one-dimensional interacting-electron models, such as the gology and Hubbard models, is discussed. On the basis of the results borrowed from previous renormalization-group results for the sine-Gordon model, different aspects of Luttinger liquid systems are described, such as the nature of the excitations and phase transitions. The calculations are thoroughly and pedagogically described, to even reach the reader with no previous experience with the sine-Gordon model or the renormalization group approach. 2013 artículo científico 0103-9733 https://www.redalyc.org/articulo.oa?id=46426434008 en http://www.redalyc.org/revista.oa?id=464 Brazilian Journal of Physics application/pdf Sociedade Brasileira de Física Brazilian Journal of Physics (Brasil) Num.3 Vol.43 |
| title | Sine-Gordon Model: Renormalization Group Solution and Applications |
| topic | Física, Astronomía y Matemáticas Sine Kosterlitz ology model Gordon model Hubbard model |
| url | https://www.redalyc.org/articulo.oa?id=46426434008 |