The t-t'-J model (strongly interacting limit of a particular Hubbard model) is solved exactly on small clusters of eight sites with periodic boundary conditions for the simple-, body-centered-, and face-centered-cubic lattices and for the two-dimensional square lattice. The symmetry, k vector, and spin of the ground state are studied as functions of crystalline environment, interaction strength, and electron concentration. Phase diagrams are presented for stable solutions, and regions of parameter space that exhibit ferromagnetism and heavy-fermionic behavior are identified.The t-t'-J model (strongly interacting limit of a particular Hubbard model) is solved exactly on small clusters of eight sites with periodic boundary conditions for the simple-, body-centered-, and face-centered-cubic lattices and for the two-dimensional square lattice. The symmetry, k vector, and spin of the ground state are studied as functions of crystalline environment, interaction strength, and electron concentration. Phase diagrams are presented for stable solutions, and regions of parameter space that exhibit ferromagnetism and heavy-fermionic behavior are identified.

Physical review. B, Condensed matterSep 15, 199020 citations

Exact Solution for the Ground State of a One-Dimensional Quantum Lattice Gas with Coulomb-Like Interaction

Bill Sutherland

We present exact wave functions for the ground state of a lattice gas of spinless one-dimensional fermions, at filling factors of $1/M$ . The one-body hopping operator decreases exponentially. The two-body interaction is Coulomb-like: A neutralizing background is required for the system to be extensive. There is a parameter in the problem, which can be taken to be the strength of the charge. All correlation functions are evaluated, and the system is shown to have long-ranged crystalline order. For filling factor $1/2$ , the momentum distribution and pair correlation function are explicitly evaluated. There is no Fermi surface. The crystalline order parameter is evaluated.We present exact wave functions for the ground state of a lattice gas of spinless one-dimensional fermions, at filling factors of $1/M$. The one-body hopping operator decreases exponentially. The two-body interaction is Coulomb-like: A neutralizing background is required for the system to be extensive. There is a parameter in the problem, which can be taken to be the strength of the charge. All correlation functions are evaluated, and the system is shown to have long-ranged crystalline order. For filling factor $1/2$, the momentum distribution and pair correlation function are explicitly evaluated. There is no Fermi surface. The crystalline order parameter is evaluated.

Physical Review LettersMar 16, 19982 citations

A quantum many-body problem in two dimensions: ground state

Avinash Khare, Koushik Ray

arXiv:hep-th/9609025Physics Letters AJun 1, 199731 citations

Ground State of the Many-Electron System

Pure and applied physicsJan 1, 19700 citations

Symmetry properties of the ground state of the system of interacting spinless bosons

Maksim Tomchenko

We perform the symmetry analysis of the properties of the ground state of a finite system of interacting spinless bosons for the three most symmetric boundary conditions (BCs): zero BCs with spherical and circular symmetries, as well as periodic BCs. The symmetry of the system can lead to interesting properties. For instance, the density of a periodic Bose system is an exact constant: ρ(r) = const. Moreover, in the case of perfect spherical symmetry of BCs, the crystalline state cannot produce the Bragg peaks. The main result of the article is that symmetry properties and general quantum-mechanical theorems admit equally both crystalline and liquid ground state for a Bose system of any density.We perform the symmetry analysis of the properties of the ground state of a finite system of interacting spinless bosons for the three most symmetric boundary conditions (BCs): zero BCs with spherical and circular symmetries, as well as periodic BCs. The symmetry of the system can lead to interesting properties. For instance, the density of a periodic Bose system is an exact constant: ρ(r) = const. Moreover, in the case of perfect spherical symmetry of BCs, the crystalline state cannot produce the Bragg peaks. The main result of the article is that symmetry properties and general quantum-mechanical theorems admit equally both crystalline and liquid ground state for a Bose system of any density.

arXiv:2112.14641Low Temperature PhysicsSep 1, 20221 citation

We present exact wave functions for the ground state of a lattice gas of spinless one-dimensional fermions, at filling factors of

1/M

. The one-body hopping operator decreases exponentially. The two-body interaction is Coulomb-like: A neutralizing background is required for the system to be extensive. There is a parameter in the problem, which can be taken to be the strength of the charge. All correlation functions are evaluated, and the system is shown to have long-ranged crystalline order. For filling factor

1/2

, the momentum distribution and pair correlation function are explicitly evaluated. There is no Fermi surface. The crystalline order parameter is evaluated.