Based on an exact treatment of hard-core bosons confined on one-dimensional lattices, we obtain the large distance behavior of the one-particle density matrix, and show how it determines the occupation of the lowest natural orbital in the thermodynamic limit. We also study the occupation ${\ensuremath{\lambda}}_{\ensuremath{\eta}}$ of the natural orbitals for large-$\ensuremath{\eta}$ at low densities. Both quantities show universal behavior independently of the confining potential. Finite-size corrections and the momentum distribution function for finite systems are also analyzed.Based on an exact treatment of hard-core bosons confined on one-dimensional lattices, we obtain the large distance behavior of the one-particle density matrix, and show how it determines the occupation of the lowest natural orbital in the thermodynamic limit. We also study the occupation ${\ensuremath{\lambda}}_{\ensuremath{\eta}}$ of the natural orbitals for large-$\ensuremath{\eta}$ at low densities. Both quantities show universal behavior independently of the confining potential. Finite-size corrections and the momentum distribution function for finite systems are also analyzed.

arXiv:cond-mat/0403078Physical Review ASep 27, 2004110 citations

Orbital phases of the lattice $p$ -band bosons

W. Vincent Liu

Bulletin of the American Physical SocietyJun 7, 20070 citations

Natural orbitals and their occupation numbers for free anyons in the magnetic gauge

Jerzy Ciosłowski, Oliver M. Brown, Tomasz Maciążek

We investigate the properties of natural orbitals and their occupation numbers of the ground state of two noninteracting anyons characterized by the fractional statistics parameter α and confined in a harmonic trap. We work in the boson magnetic gauge where the anyons are modeled as composite bosons with magnetic flux quanta attached to their positions. We derive an asymptotic form of the weakly occupied natural orbitals, and show that their corresponding (ordered descendingly) occupation numbers decay according to the power law n−(4+2α) , where n is the index of the natural orbital. We find remarkable numerical agreement of the theory with the natural orbitals and their occupation numbers computed from the spectral decomposition of the system's wave function. We explain that the same results apply to the fermion magnetic gauge. Published by the American Physical Society 2024We investigate the properties of natural orbitals and their occupation numbers of the ground state of two noninteracting anyons characterized by the fractional statistics parameter α and confined in a harmonic trap. We work in the boson magnetic gauge where the anyons are modeled as composite bosons with magnetic flux quanta attached to their positions. We derive an asymptotic form of the weakly occupied natural orbitals, and show that their corresponding (ordered descendingly) occupation numbers decay according to the power law n−(4+2α) , where n is the index of the natural orbital. We find remarkable numerical agreement of the theory with the natural orbitals and their occupation numbers computed from the spectral decomposition of the system's wave function. We explain that the same results apply to the fermion magnetic gauge. Published by the American Physical Society 2024

arXiv:2309.14023Physical Review AFeb 9, 20241 citation

Ground-state properties of hard-core bosons confined on one-dimensional optical lattices

Marcos Rigol, Alejandro Muramatsu

We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the large distance behavior of the one-particle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the low-density limit in the lattice is studied systematically, and the results obtained compared with the ones known for the hard-core boson gas without the lattice.We study the ground-state properties of hard-core bosons trapped by arbitrary confining potentials on one-dimensional optical lattices. A recently developed exact approach based on the Jordan-Wigner transformation is used. We analyze the large distance behavior of the one-particle density matrix, the momentum distribution function, and the lowest natural orbitals. In addition, the low-density limit in the lattice is studied systematically, and the results obtained compared with the ones known for the hard-core boson gas without the lattice.

arXiv:cond-mat/0409132Physical Review AJul 5, 2005111 citations