Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physics of the Solid State

Two-particle correlations in 1D-lattice systems with δ-interactions

ARMEN N. KOCHARIAN, A. S. Saakyan

Published Feb 1, 1998• 2 citations
Publisher

Abstract

The problem of two interacting particles in finite closed and open chains is solved by the Lifshitz method. The “density-density” correlation function, the dependence of the “surface” energy on the two-particle interaction energy and number of links in the chain, and the two-particle distribution on the chain are found and the nature of the ground state is clarified.

DOI
10.1134/1.1130305

Related papers

Two-particle correlations on a 1D lattice in a constant magnetic field

A. S. Saakyan

The problem of two particles interacting through the Hubbard potential on a 1 D finite lattice in a constant uniform magnetic field is solved. Exact wave functions are determined, and an equation for the energy spectrum is constructed and analyzed. The possibility of a field-induced singlet-triplet transition is demonstrated.

Physics of the Solid State•May 1, 2000•0 citations

Tight-binding electrons on open chains: Density distribution and correlations

U. Busch, K. A. Penson

The ground state of the tight-binding electrons on finite open chains is studied for arbitrary band filling. Analytic expressions for the distribution of electron density and the density-density correlation functions within the system are found and discussed as a function of chain size. Particular attention is paid to the study of boundary effects.

Physical review. B, Condensed matter•Dec 15, 1987•17 citations

Interacting Fermions in One Dimension. I. Repulsive Potential

James McGuire

The exact energies and wavefunctions for the ground state and low-lying excited states of a system of N − 1 one-dimensional fermions all of the same spin and one fermion of the opposite spin are calculated in the large-volume, finite-density limit when the particles interact via a repulsive delta function potential. A number of properties of the system such as pair correlation functions and the effective mass of a certain class of excitations are also discussed.

Journal of Mathematical Physics•Mar 1, 1965•220 citations

One-Dimensional Chain of Anisotropic Spin-Spin Interactions. III. Applications

Chongming Yang, Chuan‐Zhang Yang

The magnetization---versus---magnetic-field curve of the one-dimensional chain at $T=0$ is discussed. Also, the corresponding $p\ensuremath{-}V$ diagram of the quantum lattice gas (q.l.g.) is discussed. The ground-state wave function for the case $\ensuremath{\Delta}>1$, in a q.l.g. of a finite number of particles on an infinite lattice is analyzed in detail, giving the "surface energy" near the ends. In the Appendix some general properties of the q.l.g. in one, two, or three dimensions are given.

Physical Review•Nov 4, 1966•379 citations

Exploiting the links between ground-state correlations and independent-fermion entropy in the Hubbard model

T. S. Müller, W. Töws, G. M. Pastor

The ground-state properties of the half-filled Hubbard model are investigated in the framework of lattice density functional theory. The single-particle density matrix ${\ensuremath{\gamma}}_{ij\ensuremath{\sigma}}$ is regarded as the central variable of the many-body problem, where $i$ and $j$ refer to the lattice sites and $\ensuremath{\sigma}$ to the spin. The interaction-energy functional $W[{\ensuremath{\gamma}}_{ij\ensuremath{\sigma}}]$ is calculated exactly for representative finite periodic systems by performing exact Lanczos diagonalizations. The relationship between $W[{\ensuremath{\gamma}}_{ij\ensuremath{\sigma}}]$ and the entropy $S[{\ensuremath{\eta}}_{\mathbit{k}\ensuremath{\sigma}}]$ of independent fermions with natural-orbital occupations ${\ensuremath{\eta}}_{\mathbit{k}\ensuremath{\sigma}}$ is analyzed. A simple approximation to the interaction energy of the half-filled Hubbard model is proposed, which takes the form $W=W(S[{\ensuremath{\eta}}_{\mathbit{k}\ensuremath{\sigma}}])$. Using this functional we derive the ground-state energy, kinetic energy, average number of double occupations, charge distribution, magnetic susceptibility, and field-induced spin polarization in one-, two-, and three-dimensional periodic lattices. The limit of infinite dimensions is also explored. The accuracy of the method is assessed by comparison with available exact numerical or analytical results. Goals, limitations, and possible extensions of the domain of applicability of the functional are discussed.

Physical review. B./Physical review. B•Jul 26, 2018•7 citations

Correlation functions in a one-dimensional Bose gas

Anatoli G. Izergin, V. E. Korepin, Nicolai Reshetikhin

The problem of calculating correlation functions is considered for the one-dimensional Bose gas with a delta-function repulsive interaction between particles. The method of calculation is based on the algebraic Bethe ansatz.

Journal of Physics A Mathematical and General•Oct 1, 1987•49 citations
The problem of two interacting particles in finite closed and open chains is solved by the Lifshitz method. The “density-density” correlation function, the dependence of the “surface” energy on the two-particle interaction energy and number of links in the chain, and the two-particle distribution on the chain are found and the nature of the ground state is clarified.
The magnetization---versus---magnetic-field curve of the one-dimensional chain at T=0T=0T=0 is discussed. Also, the corresponding $p\ensuremath{-}V$ diagram of the quantum lattice gas (q.l.g.) is discussed. The ground-state wave function for the case $\ensuremath{\Delta}>1$, in a q.l.g. of a finite number of particles on an infinite lattice is analyzed in detail, giving the "surface energy" near the ends. In the Appendix some general properties of the q.l.g. in one, two, or three dimensions are given.
The ground-state properties of the half-filled Hubbard model are investigated in the framework of lattice density functional theory. The single-particle density matrix ${\ensuremath{\gamma}}_{ij\ensuremath{\sigma}}$ is regarded as the central variable of the many-body problem, where iii and jjj refer to the lattice sites and $\ensuremath{\sigma}$ to the spin. The interaction-energy functional $W[{\ensuremath{\gamma}}_{ij\ensuremath{\sigma}}]$ is calculated exactly for representative finite periodic systems by performing exact Lanczos diagonalizations. The relationship between $W[{\ensuremath{\gamma}}_{ij\ensuremath{\sigma}}]$ and the entropy $S[{\ensuremath{\eta}}_{\mathbit{k}\ensuremath{\sigma}}]$ of independent fermions with natural-orbital occupations ${\ensuremath{\eta}}_{\mathbit{k}\ensuremath{\sigma}}$ is analyzed. A simple approximation to the interaction energy of the half-filled Hubbard model is proposed, which takes the form $W=W(S[{\ensuremath{\eta}}_{\mathbit{k}\ensuremath{\sigma}}])$. Using this functional we derive the ground-state energy, kinetic energy, average number of double occupations, charge distribution, magnetic susceptibility, and field-induced spin polarization in one-, two-, and three-dimensional periodic lattices. The limit of infinite dimensions is also explored. The accuracy of the method is assessed by comparison with available exact numerical or analytical results. Goals, limitations, and possible extensions of the domain of applicability of the functional are discussed.