The chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition
Abstract We study the phase diagram of the (1 + 1)-dimensional Gross-Neveu model with both g x 2 ψ ¯ ψ 2 $$ {g}_x^2{\left(\overline{\psi}\psi \right)}^2 $$ and g y 2 ψ ¯ i γ 5 ψ 2 $$ {g}_y^2{\left(\overline{\psi}i{\gamma}_5\psi \right)}^2 $$ interaction terms on a spatial lattice. The continuous chi...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-06-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP06(2022)019 |
| _version_ | 1797865735389708288 |
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| author | Gertian Roose Jutho Haegeman Karel Van Acoleyen Laurens Vanderstraeten Nick Bultinck |
| author_facet | Gertian Roose Jutho Haegeman Karel Van Acoleyen Laurens Vanderstraeten Nick Bultinck |
| author_sort | Gertian Roose |
| collection | DOAJ |
| description | Abstract We study the phase diagram of the (1 + 1)-dimensional Gross-Neveu model with both g x 2 ψ ¯ ψ 2 $$ {g}_x^2{\left(\overline{\psi}\psi \right)}^2 $$ and g y 2 ψ ¯ i γ 5 ψ 2 $$ {g}_y^2{\left(\overline{\psi}i{\gamma}_5\psi \right)}^2 $$ interaction terms on a spatial lattice. The continuous chiral symmetry, which is present in the continuum model when g x 2 = g y 2 $$ {g}_x^2={g}_y^2 $$ , has a mixed ’t Hooft anomaly with the charge conservation symmetry, which guarantees the existence of a massless mode. However, the same ’t Hooft anomaly also implies that the continuous chiral symmetry is broken explicitly in our lattice model. Nevertheless, from numerical matrix product state simulations we find that for certain parameters of the lattice model, the continuous chiral symmetry reemerges in the infrared fixed point theory, even at strong coupling. We argue that, in order to understand this phenomenon, it is crucial to go beyond mean-field theory (or, equivalently, beyond the leading order term in a 1/N expansion). Interestingly, on the lattice, the chiral Gross-Neveu model appears at a Landau-forbidden second order phase transition separating two distinct and unrelated symmetry-breaking orders. We point out the crucial role of two different ’t Hooft anomalies or Lieb-Schultz-Mattis obstructions for this Landau-forbidden phase transition to occur. |
| first_indexed | 2024-04-09T23:12:58Z |
| format | Article |
| id | doaj.art-4fc0b199e1c74742be91c9edd7b8c6a2 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:12:58Z |
| publishDate | 2022-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-4fc0b199e1c74742be91c9edd7b8c6a22023-03-22T10:14:24ZengSpringerOpenJournal of High Energy Physics1029-84792022-06-012022612910.1007/JHEP06(2022)019The chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transitionGertian Roose0Jutho Haegeman1Karel Van Acoleyen2Laurens Vanderstraeten3Nick Bultinck4Department of Physics and Astronomy, University of GhentDepartment of Physics and Astronomy, University of GhentDepartment of Physics and Astronomy, University of GhentDepartment of Physics and Astronomy, University of GhentDepartment of Physics and Astronomy, University of GhentAbstract We study the phase diagram of the (1 + 1)-dimensional Gross-Neveu model with both g x 2 ψ ¯ ψ 2 $$ {g}_x^2{\left(\overline{\psi}\psi \right)}^2 $$ and g y 2 ψ ¯ i γ 5 ψ 2 $$ {g}_y^2{\left(\overline{\psi}i{\gamma}_5\psi \right)}^2 $$ interaction terms on a spatial lattice. The continuous chiral symmetry, which is present in the continuum model when g x 2 = g y 2 $$ {g}_x^2={g}_y^2 $$ , has a mixed ’t Hooft anomaly with the charge conservation symmetry, which guarantees the existence of a massless mode. However, the same ’t Hooft anomaly also implies that the continuous chiral symmetry is broken explicitly in our lattice model. Nevertheless, from numerical matrix product state simulations we find that for certain parameters of the lattice model, the continuous chiral symmetry reemerges in the infrared fixed point theory, even at strong coupling. We argue that, in order to understand this phenomenon, it is crucial to go beyond mean-field theory (or, equivalently, beyond the leading order term in a 1/N expansion). Interestingly, on the lattice, the chiral Gross-Neveu model appears at a Landau-forbidden second order phase transition separating two distinct and unrelated symmetry-breaking orders. We point out the crucial role of two different ’t Hooft anomalies or Lieb-Schultz-Mattis obstructions for this Landau-forbidden phase transition to occur.https://doi.org/10.1007/JHEP06(2022)019Chiral SymmetryEffective Field TheoriesPhase Transitions |
| spellingShingle | Gertian Roose Jutho Haegeman Karel Van Acoleyen Laurens Vanderstraeten Nick Bultinck The chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition Journal of High Energy Physics Chiral Symmetry Effective Field Theories Phase Transitions |
| title | The chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition |
| title_full | The chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition |
| title_fullStr | The chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition |
| title_full_unstemmed | The chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition |
| title_short | The chiral Gross-Neveu model on the lattice via a Landau-forbidden phase transition |
| title_sort | chiral gross neveu model on the lattice via a landau forbidden phase transition |
| topic | Chiral Symmetry Effective Field Theories Phase Transitions |
| url | https://doi.org/10.1007/JHEP06(2022)019 |
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