Exact ground-state properties of one-dimensional electron gas at high density

Abstract

The dynamical response theory is used to obtain an analytical expression for the exchange energy of a quantum wire for arbitrary polarization and width. It reproduces the known form of exchange energy for 1D electron gas in the limit of infinitely thin cylindrical and harmonic wires. The structure factor for these wires are also obtained analytically in the high-density or small $r_s$ limit. This structure factor enables us to get the {\it exact} correlation energy for both the wires and demonstrates that there are at least two methods to get the ideal Coulomb limit in one dimension. The structure factor and the correlation energy are found to be independent of the way the one-dimensional Coulomb potential is regularized. The analytical expression for the pair correlation function is also presented for small distances and provides a justification for the small $r_s$ expansion as long as $r_s<\frac{3}{2}\left(\frac{{\pi }^2}{{\pi }^2+3}\right)=1.15$.

References in corpus (18)

• Luttinger Liquid Behavior in Carbon Nanotubes
• Wigner Crystal in One Dimension
• Confinement induced molecules in a 1D Fermi gas
• New Model System for a One-Dimensional Electron Liquid: Self-Organized Atomic Gold Chains on Ge(001)
• Ground state properties of the one dimensional Coulomb gas
• Is a Trapped One-Dimensional Bose Gas a Luttinger Liquid?
• Exact wave functions of two-electron quantum rings
• Ground-state energy of the electron liquid in ultrathin wires
• Exact ground state properties of the one-dimensional Coulomb gas
• How universal is the fractional-quantum-Hall edge Luttinger liquid?
• Fermi 1D quantum gas: Luttinger liquid approach and spin-charge separation
• Ground state properties of the one-dimensional electron liquid
• Uniform electron gases. I. Electrons on a ring
• Invariance of the correlation energy at high density and large dimension in two-electron systems
• High-density correlation energy expansion of the one-dimensional uniform electron gas
• Short-range correlations and spin-mode velocities in ultrathin one-dimensional conductors
• Dependence of structure factor and correlation energy on the width of electron wires
• One-dimensional electron fluid at high density

Cited by in corpus (5)

• Electron correlation and confinement effects in quasi-one-dimensional quantum wires at high density
• Ground-state properties of electron-electron biwire systems
• Wire width and density dependence of the crossover in the peak of the static structure factor from $2k_{\text{F}}$ $\to$ $4k_{\text{F}}$ in one-dimensional paramagnetic electron gases
• Electronic quantum wires in extended quasiparticle picture
• Off-shell selfenergy for 1-D Fermi liquids