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<p>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 +1<i>d</i>, and find precise agreement with integrability results when the scaling dimension ∆ of the deforming cosine/cosinh potential is in the range ∆ ≤ 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 (∆ &lt; 0), which relates ∆ ↔ 4/∆. As the dimension approaches the upper limit ∆ = 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 ∆ &gt; 1.</p>

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Toolkit for general 2d scalar potential in LCT

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月19日

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  • A. Liam Fitzpatrick,
  • Emanuel Katz,
  • Yuan Xin

摘要

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 ∆ of the deforming cosine/cosinh potential is in the range ∆ ≤ 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 (∆ < 0), which relates ∆ ↔ 4/∆. As the dimension approaches the upper limit ∆ = 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 ∆ > 1.