Imaginary-time nonuniform mesh method for solving the multidimensional Schrodinger equation: Fermionization and melting of quantum Lennard-Jones crystals
arXiv:1304.8015 · doi:10.1103/PhysRevA.88.062107
Abstract
An imaginary-time nonuniform mesh method is presented and used to find the first 50 eigenstates and energies of up to five strongly interacting spinless quantum Lennard-Jones particles trapped in a one-dimensional harmonic potential. We show that the use of tailored grids reduces drastically the computational effort needed to diagonalize the Hamiltonian and results in a favorable scaling with dimensionality. Solutions to both bosonic and fermionic counterparts of this strongly interacting system are obtained, the bosonic case clustering as a Tonks-Girardeau crystal exhibiting the phenomenon of fermionization. The numerically exact excited states are used to describe the melting of this crystal at finite temperature.
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