Description
Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. In this talk, I will show how to treat Hamiltonian truncation systematically using effective field theory methodology. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states below some energy cutoff Emax. The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of 1/Emax. This method is demonstrated using 2D lambda phi^4 theory, and gives 1/Emax^2 corrections to the effective Hamiltonian. Numerical diagonalization of the effective Hamiltonian then shows residual errors of order 1/Emax^3, as expected by our power counting.
