Wilson-Fisher fixed points in presence of Dirac fermions
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866910915707797504 |
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| author | Herbut, Igor F. |
| author_facet | Herbut, Igor F. |
| contents | Wilson-Fisher expansion near upper critical dimension has proven to be an invaluable conceptual and computational tool in our understanding of the universal critical behavior in the $ϕ^4$ field theories that describe low-energy physics of the canonical models such as Ising, XY, and Heisenberg. Here I review its application to a class of the Gross-Neveu-Yukawa (GNY) field theories, which emerge as possible universal description of a number of quantum phase transitions in electronic two-dimensional systems such as graphene and d-wave superconductors. GNY field theories may be viewed as minimal modifications of the $ϕ^4$ field theories in which the order parameter is coupled to relativistic Dirac fermions through Yukawa term, and which still exhibit critical fixed points in the suitably formulated Wilson-Fisher $ε$-expansion. I discuss the unified GNY field theory for a set of different symmetry-breaking patterns, with focus on the semimetal-Néel-ordered-Mott insulator quantum phase transition in the half-filled Hubbard model on the honeycomb lattice, for which a comparison between the state-of-the-art $ε$-expansion, quantum Monte Carlo, large-N, and functional renormalization group calculations can be made. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_07654 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Wilson-Fisher fixed points in presence of Dirac fermions Herbut, Igor F. Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Wilson-Fisher expansion near upper critical dimension has proven to be an invaluable conceptual and computational tool in our understanding of the universal critical behavior in the $ϕ^4$ field theories that describe low-energy physics of the canonical models such as Ising, XY, and Heisenberg. Here I review its application to a class of the Gross-Neveu-Yukawa (GNY) field theories, which emerge as possible universal description of a number of quantum phase transitions in electronic two-dimensional systems such as graphene and d-wave superconductors. GNY field theories may be viewed as minimal modifications of the $ϕ^4$ field theories in which the order parameter is coupled to relativistic Dirac fermions through Yukawa term, and which still exhibit critical fixed points in the suitably formulated Wilson-Fisher $ε$-expansion. I discuss the unified GNY field theory for a set of different symmetry-breaking patterns, with focus on the semimetal-Néel-ordered-Mott insulator quantum phase transition in the half-filled Hubbard model on the honeycomb lattice, for which a comparison between the state-of-the-art $ε$-expansion, quantum Monte Carlo, large-N, and functional renormalization group calculations can be made. |
| title | Wilson-Fisher fixed points in presence of Dirac fermions |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2304.07654 |