Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866912757727625216 |
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| author | Lang, Thomas C. Läuchli, Andreas M. |
| author_facet | Lang, Thomas C. Läuchli, Andreas M. |
| contents | We perform large scale quantum Monte Carlo simulations of the Hubbard model at half filling with a single Dirac cone close to the critical point, which separates a Dirac semi-metal from an antiferromagnetically ordered phase where SU(2) spin rotational symmetry is spontaneously broken. We discuss the implementation of a single Dirac cone in the SLAC formulation for eight Dirac components and the influence of dynamically induced long-range super-exchange interactions. The finite size behavior of dimensionless ratios and the finite size scaling properties of the Hubbard model with a single Dirac cone are shown to be superior compared to the honeycomb lattice. We extract the critical exponent believed to belong to the chiral Heisenberg Gross-Neveu-Yukawa universality class: The critical exponent ${ν= 1.02(3)}$ coincides for the two lattice types once honeycomb lattices of linear dimension ${L\ge 15}$ are considered. In contrast to the SLAC formulation, where the anomalous dimensions are estimated to be ${η_ϕ=0.73(1)}$ and ${η_ψ=0.09(1)}$, they remain less stable on honeycomb lattices, but tend towards the estimates from the SLAC formulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_15000 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions Lang, Thomas C. Läuchli, Andreas M. Strongly Correlated Electrons High Energy Physics - Lattice We perform large scale quantum Monte Carlo simulations of the Hubbard model at half filling with a single Dirac cone close to the critical point, which separates a Dirac semi-metal from an antiferromagnetically ordered phase where SU(2) spin rotational symmetry is spontaneously broken. We discuss the implementation of a single Dirac cone in the SLAC formulation for eight Dirac components and the influence of dynamically induced long-range super-exchange interactions. The finite size behavior of dimensionless ratios and the finite size scaling properties of the Hubbard model with a single Dirac cone are shown to be superior compared to the honeycomb lattice. We extract the critical exponent believed to belong to the chiral Heisenberg Gross-Neveu-Yukawa universality class: The critical exponent ${ν= 1.02(3)}$ coincides for the two lattice types once honeycomb lattices of linear dimension ${L\ge 15}$ are considered. In contrast to the SLAC formulation, where the anomalous dimensions are estimated to be ${η_ϕ=0.73(1)}$ and ${η_ψ=0.09(1)}$, they remain less stable on honeycomb lattices, but tend towards the estimates from the SLAC formulation. |
| title | Chiral Heisenberg Gross-Neveu-Yukawa criticality: Honeycomb vs. SLAC fermions |
| topic | Strongly Correlated Electrons High Energy Physics - Lattice |
| url | https://arxiv.org/abs/2503.15000 |