Papers › Toolkit for General 2d Scalar Potential in LCT
Toolkit for General 2d Scalar Potential in LCT
A. Liam Fitzpatrick, Emanuel Katz, Yuan Xin
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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≤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↔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.
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