Imaginary-time nonuniform mesh method for solving the multidimensional Schrodinger equation: Fermionization and melting of quantum Lennard-Jones crystals

TL;DR

This paper introduces an imaginary-time nonuniform mesh method to efficiently compute eigenstates of strongly interacting quantum particles, revealing fermionization and melting phenomena in quantum Lennard-Jones crystals.

Contribution

The paper presents a novel nonuniform mesh approach that significantly reduces computational effort in solving multidimensional Schrödinger equations for strongly interacting particles.

Findings

Efficient computation of first 50 eigenstates for up to five particles.

Observation of fermionization in bosonic systems.

Description of crystal melting at finite temperature.

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.