Eur. Phys. J. A (2019) 55: 144
https://doi.org/10.1140/epja/i2019-12844-9

Regular Article - Theoretical Physics

Adiabatic projection method with Euclidean time subspace projection

Faculty of Engineering, Karamanoglu Mehmetbey University, 70100, Karaman, Turkey

^* e-mail: serdarelhatisari@kmu.edu.tr

Received: 3 June 2019
Accepted: 29 July 2019
Published online: 30 August 2019

Abstract

Euclidean time projection is a powerful tool that uses exponential decay to extract the low-energy information of quantum systems. The adiabatic projection method, which is based on Euclidean time projection, is a procedure for studying scattering and reactions on the lattice. The method constructs the adiabatic Hamiltonian that gives the low-lying energies and wave functions of two-cluster systems. In this paper we seek the answer to the question whether an adiabatic Hamiltonian constructed in a smaller subspace of the two-cluster state space can still provide information on the low-lying spectrum and the corresponding wave functions. We present the results from our investigations on constructing the adiabatic Hamiltonian using Euclidean time projection and extracting details of the low-energy spectrum and wave functions by diagonalizing it. In our analyses we consider systems of fermion-fermion and fermion-dimer interacting via a zero-range attractive potential in one dimension, and fermion-fermion interacting via an attractive Gaussian potential in three dimensions. The results presented here provide a guide for improving the adiabatic projection method and for reducing the computational costs of large-scale calculations of ab initio nuclear scattering and reactions using Monte Carlo methods.