2013/04/30 by Alberto Hernando, Jiří Vaníček, Jiri Vanicek
Mathematics · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #Curse of dimensionality #Degeneracy (biology) #Eigenvalues and eigenvectors #Excited state #Hamiltonian (control theory) #Imaginary time #Mathematics #Physics #Quantum #Quantum dynamics #Quantum many-body systems #Quantum mechanics #Quantum, superfluid, helium dynamics #Statistical physics #quant-ph
paper · pdf · doi:10.1103/physreva.88.062107
published as Phys. Rev. A 88, 062107 (2013)
arxiv created 2013/06/09 · openalex publication_date 2013/12/18 · openalex created_date 2016/06/24 · arxiv updated 2017/05/10 · openalex updated_date 2026/08/05
An imaginary-time nonuniform mesh method for diagonalizing multidimensional quantum Hamiltonians is proposed and used to find the first 50 eigenstates and energies of up to D=5 strongly interacting spinless quantum Lennard-Jones particles trapped in a one-dimensional harmonic potential. We show that the use of tailored grids allows exploitation of the symmetries of the system (in our case the D! degeneracy derived from all possible permutations of distinguishable particles), reducing drastically the computational effort needed to diagonalize the Hamiltonian. This leads to a favorable scaling with dimensionality, requiring for the five-dimensional system four orders of magnitude fewer grid points than the equivalent regular grid. Solutions to both bosonic and fermionic counterparts of this strongly interacting system are constructed, 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.