Adiabatic projection method for scattering and reactions on the lattice

TL;DR

The paper introduces the adiabatic projection method, a new framework for calculating scattering and reactions on the lattice, demonstrating its accuracy with neutron-deuteron scattering results.

Contribution

It presents the adiabatic projection method for lattice scattering calculations and validates it with a neutron-deuteron scattering example, showing high accuracy in reproducing known results.

Findings

Spectrum of the adiabatic Hamiltonian matches the original below inelastic threshold.

Calculated s-wave phase shift agrees with the exact continuum result.

Method can be extended to inelastic reactions with multiple channels.

Abstract

We demonstrate and test the adiabatic projection method, a general new framework for calculating scattering and reactions on the lattice. The method is based upon calculating a low-energy effective theory for clusters which becomes exact in the limit of large Euclidean projection time. As a detailed example we calculate the adiabatic two-body Hamiltonian for elastic fermion-dimer scattering in lattice effective field theory. Our calculation corresponds to neutron-deuteron scattering in the spin-quartet channel at leading order in pionless effective field theory. We show that the spectrum of the adiabatic Hamiltonian reproduces the spectrum of the original Hamiltonian below the inelastic threshold to arbitrary accuracy. We also show that the calculated s-wave phase shift reproduces the known exact result in the continuum and infinite-volume limits. When extended to more than one scattering channel, the adiabatic projection method can be used to calculate inelastic reactions on the lattice in future work.