Form Factors and Spectral Densities from Lightcone Conformal Truncation

TL;DR

This paper employs Lightcone Conformal Truncation to compute form factors and spectral densities of local operators in 2D $\

Contribution

It introduces methods to accurately extract form factors and spectral densities using LCT, reducing truncation errors and enabling analysis at various momenta.

Findings

Successfully computed form factors between single-particle states.

Achieved rapid convergence of two-point functions away from branch cuts.

Demonstrated extraction of spectral densities at branch cuts.

Abstract

We use the method of Lightcone Conformal Truncation (LCT) to obtain form factors and spectral densities of local operators $\mathcal{O}$ in $\phi^4$ theory in two dimensions. We show how to use the Hamiltonian eigenstates from LCT to obtain form factors that are matrix elements of a local operator $\mathcal{O}$ between single-particle bra and ket states, and we develop methods that significantly reduce errors resulting from the finite truncation of the Hilbert space. We extrapolate these form factors as a function of momentum to the regime where, by crossing symmetry, they are form factors of $\mathcal{O}$ between the vacuum and a two-particle asymptotic scattering state. We also compute the momentum-space time-ordered two-point functions of local operators in LCT. These converge quickly at momenta away from branch cuts, allowing us to indirectly obtain the time-ordered correlator and the spectral density at the branch cuts. We focus on the case where the local operator $\mathcal{O}$ is the trace $\Theta$ of the stress tensor.