Lightcone Hamiltonian for Ising Field Theory I: T < T_c

Abstract

We study 2d Ising Field Theory (IFT) in the low-temperature phase in lightcone quantization, and show that integrating out zero modes generates a very compact form for the effective lightcone interaction that depends on the finite volume vacuum expectation value of the $\sigma$ operator. This form is most naturally understood in a conformal basis for the lightcone Hilbert space. We further verify that this simple form reproduces to high accuracy results for the spectra, the $c$-function, and the form-factors from integrability methods for the magnetic deformation of IFT. For generic non-integrable values of parameters we also compute the above observables and compare our numeric results to those of equal-time truncation. In particular, we report on new measurements of various bound-state form-factors as well as the stress-tensor spectral density. We find that the stress tensor spectral density provides additional evidence that certain resonances of IFT are surprisingly narrow, even at generic strong coupling. Explicit example code for constructing the effective Hamiltonian is included in an appendix.

55 pages, 10 figures. v2: minor fixes. v3: minor revision

References in corpus (10)

• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions
• The Spin-Spin Correlation Function in the Two-Dimensional Ising Model in a Magnetic Field at $T=T_c$
• Signatures of rare states and thermalization in a theory with confinement
• NLO Renormalization in the Hamiltonian Truncation
• Lightcone Effective Hamiltonians and RG Flows
• Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data
• Form Factors and Spectral Densities from Lightcone Conformal Truncation
• Ising Spectroscopy I: Mesons at T < T_c
• Large Momentum EFT and Lightcone Quantization
• Toolkit for General 2d Scalar Potential in LCT