Ground states of hard-core bosons in one dimensional periodic potentials

Abstract

With Girardeau's Fermi-Bose mapping, we find the exact ground states of hard-core bosons residing in a one dimensional periodic potential. The analysis of these ground states shows that when the number of bosons $N$ is commensurate with the number of wells $M$ in the periodic potential, the boson system is a Mott insulator whose energy gap, however, is given by the single-particle band gap of the periodic potential; when $N$ is not commensurate with $M$, the system is a metal (not a superfluid). In fact, we argue that there may be no superfluid phase for any one-dimensional boson system in terms of Landau's criterion of superfluidity. The Kronig-Penney potential is used to illustrate our results.

6 pages, 6 figures

References in corpus (8)

• Hard-core bosons on optical superlattices: Dynamics and relaxation in the superfluid and insulating regimes
• Exact coherent states of a harmonically confined Tonks-Girardeau gas
• Fermionization in an expanding 1D gas of hard-core bosons
• Emergence of quasi-condensates of hard-core bosons at finite momentum
• Dynamics of a Tonks-Girardeau gas released from a hard-wall trap
• Decay by tunneling of Bosonic and Fermionic Tonks-Girardeau Gases
• Momentum distribution for a one-dimensional trapped gas of hard-core bosons
• Off-diagonal correlations of lattice impenetrable bosons in one dimension

Cited by in corpus (11)

• Cold Bosons in Optical Lattices
• Boson Pairs in a One-dimensional Split Trap
• Ground-state properties of few-Boson system in a one-dimensional hard wall potential with split
• Correlation versus commensurability effects for finite bosonic systems in one-dimensional lattices
• Optical lattices as a tool to study defect-induced superfluidity
• Low-energy excitations of a boson pair in a double-well trap
• The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas
• Ground state properties of a Tonks-Girardeau Gas in a periodic potential
• Spin-flip induced superfluidity in a ring of spinful hard-core bosons
• One Dimensional Magnetized TG Gas Properties in an External Magnetic Field
• Probing the thermal atoms of a Bose gas through Raman transition