A Bethe ansatz study of the ground state energy for the repulsive Bose–Hubbarddimer

Abstract

We employ an exact Bethe ansatz solution to study the repulsive Bose–Hubbard dimermodel. Using a continuum approximation we solve for the ground state root density and inturn compute the ground state energy per particle. The formula so obtained is accurate fora finite-sized system in the weak coupling limit. Surprisingly, the formula diverges from thenumerically calculated value as the number of particles increases. This indicates that theformula fails to predict the ground state energy per particle in the thermodynamiclimit.