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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.12255 |
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| _version_ | 1866909609851092992 |
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| author | Fitzpatrick, A. Liam Katz, Emanuel Xin, Yuan |
| author_facet | Fitzpatrick, A. Liam Katz, Emanuel Xin, Yuan |
| contents | We present efficient algorithms for obtaining the Hamiltonian in Lightcone Conformal Truncation (LCT) for a 2d scalar field with a generic potential. We apply this method to the sine-Gordon and sinh-Gordon models in $1+1d$, and find precise agreement with integrability results when the scaling dimension $Δ$ of the deforming cosine/cosinh potential is in the range $ Δ\leq 1$. The agreement provides additional evidence for a recent conjecture for how to compute the effective lightcone Hamiltonian in this class of models. In addition, to high precision, we provide the first direct confirmation for the conjectured self-duality of the sinh-Gordon model ($Δ< 0)$, which relates $Δ\leftrightarrow 4/Δ$. As the dimension approaches the upper limit $Δ=1$ from below, we show analytically that the Hamiltonian matrix elements exactly reproduce those of a free Majorana fermion, demonstrating how bosonization is manifested in the LCT basis. We comment on the possible extension of the approach to $Δ> 1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_12255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Toolkit for General 2d Scalar Potential in LCT Fitzpatrick, A. Liam Katz, Emanuel Xin, Yuan High Energy Physics - Theory Statistical Mechanics We present efficient algorithms for obtaining the Hamiltonian in Lightcone Conformal Truncation (LCT) for a 2d scalar field with a generic potential. We apply this method to the sine-Gordon and sinh-Gordon models in $1+1d$, and find precise agreement with integrability results when the scaling dimension $Δ$ of the deforming cosine/cosinh potential is in the range $ Δ\leq 1$. The agreement provides additional evidence for a recent conjecture for how to compute the effective lightcone Hamiltonian in this class of models. In addition, to high precision, we provide the first direct confirmation for the conjectured self-duality of the sinh-Gordon model ($Δ< 0)$, which relates $Δ\leftrightarrow 4/Δ$. As the dimension approaches the upper limit $Δ=1$ from below, we show analytically that the Hamiltonian matrix elements exactly reproduce those of a free Majorana fermion, demonstrating how bosonization is manifested in the LCT basis. We comment on the possible extension of the approach to $Δ> 1$. |
| title | Toolkit for General 2d Scalar Potential in LCT |
| topic | High Energy Physics - Theory Statistical Mechanics |
| url | https://arxiv.org/abs/2412.12255 |