Comparing numerical and analytical approaches to strongly interacting two-component mixtures in one dimensional traps

We investigate one-dimensional harmonically trapped two-component systems for repulsive interaction strengths ranging from the non-interacting to the strongly interacting regime for Fermi-Fermi mixtures. A new and powerful mapping between the interaction strength parameters from a continuous Hamiltonian and a discrete lattice Hamiltonian is derived. As an example, we show that this mapping does not depend neither on the state of the system nor on the number of particles. Energies, density profiles and correlation functions are obtained both numerically (density matrix renormalization group (DMRG) and exact diagonalization) and analytically. Since DMRG results do not converge as the interaction strength is increased, analytical solutions are used as a benchmark to identify the point where these calculations become unstable. We use the proposed mapping to set a quantitative limit on the interaction parameter of a discrete lattice Hamiltonian above which DMRG gives unrealistic results.