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

Journal of Physics A Mathematical and General

Exact results for the U= infinity Hubbard model

Andreas Mielke

Published Dec 21, 1992• 20 citations
Publisher

Abstract

The author investigates the U= infinity Hubbard model on a large class of lattices which are line graphs. The most interesting lattices in this class are line graphs of regular bipartite lattices with N s sites and coordination number k>or=4. The ground state energy and some ground states are given. If the number of electrons N satisfies N s >or=N>or=2N s /k-2, the ground state energy is -4 mod t mod (N s -N). The ground states have no magnetic ordering, they are projections of the ground states at U=0 onto the subspace of states without doubly occupied sites.

DOI
10.1088/0305-4470/25/24/006

Related papers

Ferromagnetism in the Hubbard model on line graphs and further considerations

Andreas Mielke

Let L(G) be the line graph of a graph G=(V,E). The Hubbard model on L(G) has ferromagnetic ground states with a saturated spin if the interaction is repulsive (U>0) and if the number of electrons N satisfies N>or=M. M= mod E mod + mod V mod -1 if G is bipartite and M= mod E mod + mod V mod otherwise. The author shows that the ferromagnetic ground state is unique if N=M. Further he gives a sufficient condition for the existence of other ground states if N>M. The results are valid also for a multi-band Hubbard model on a bipartite graph. In the case of a periodic lattice, the results are related to the existence of a flat energy band.

Journal of Physics A Mathematical and General•Jul 21, 1991•492 citations

Ferromagnetic ground states for the Hubbard model on line graphs

Andreas Mielke

The author discusses some of the properties of the Hubbard model on a line graph with n vertices. It is shown that the model has ferromagnetic ground states if the interaction is repulsive (U)0) and if the number of electrons N satisfies 2n>or=N>or=M. M is a natural number that depends on the line graph. For example, the Kagome lattice is a line graph, it has M=5n/3-1.

Journal of Physics A Mathematical and General•Jan 21, 1991•458 citations

Exact magnetic ground-state properties of the one-dimensional Hubbard model

Yang C; Kocharian AN; Chiang YL

[[abstract]]The exact solution of the one-dimensional Hubbard model, both attractive and repulsive, is investigated in dependence of electron concentration n over a wide range of interaction strength U and magnetic field h. The magnetic phase diagram and the ground-state properties, including the total energy, the number of double occupied sites and the kinetic energy are studied for -infinity < U < infinity and 0 less than or equal to n less than or equal to 1.

•Jan 1, 2000•0 citations

Ferromagnetism in an itinerant electron system: Hubbard model on complete graph

D. F. Wang

In this work, the ground states of the Hubbard model on complete graph are studied, for a finite lattice size $L$ and arbitrary on-site energy $U$. We construct explicitly the ground states of the system when the number of the electrons $N_e \ge L+1$. In particular, for $N_e=L+1$, the ground state is ferromagnetic with total spin $s_g=(N_e-2)/2$.

arXiv:cond-mat/9604121•Apr 18, 1996•1 citation

The ground state problem in the infinite-U Hubbard model

E. V. Kuz’min

The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ 0 (1) (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ 0(n)<ɛ FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m.

Physics of the Solid State•Feb 1, 1997•3 citations

Rigorous results on superconducting ground states for attractive extended Hubbard models

Arianna Montorsi, David K Campbell

We show that the exact ground state for a class of extended Hubbard models including bond-charge, exchange, and pair-hopping terms, is the Yang ``\ensuremath{\eta}-paired'' state for any nonvanishing positive value of the pair-hopping amplitude, at least when the on-site Coulomb interaction is attractive enough and the remaining physical parameters satisfy a single constraint. The ground state is thus rigorously superconducting. Our result holds on a bipartite lattice in any dimension, at any band filling, and for arbitrary electron hopping. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9502027•Physical review. B, Condensed matter•Mar 1, 1996•36 citations
The author investigates the U= infinity Hubbard model on a large class of lattices which are line graphs. The most interesting lattices in this class are line graphs of regular bipartite lattices with N s sites and coordination number k>or=4. The ground state energy and some ground states are given. If the number of electrons N satisfies N s >or=N>or=2N s /k-2, the ground state energy is -4 mod t mod (N s -N). The ground states have no magnetic ordering, they are projections of the ground states at U=0 onto the subspace of states without doubly occupied sites.
Let L(G) be the line graph of a graph G=(V,E). The Hubbard model on L(G) has ferromagnetic ground states with a saturated spin if the interaction is repulsive (U>0) and if the number of electrons N satisfies N>or=M. M= mod E mod + mod V mod -1 if G is bipartite and M= mod E mod + mod V mod otherwise. The author shows that the ferromagnetic ground state is unique if N=M. Further he gives a sufficient condition for the existence of other ground states if N>M. The results are valid also for a multi-band Hubbard model on a bipartite graph. In the case of a periodic lattice, the results are related to the existence of a flat energy band.
In this work, the ground states of the Hubbard model on complete graph are studied, for a finite lattice size LLL and arbitrary on-site energy UUU. We construct explicitly the ground states of the system when the number of the electrons Ne≥L+1N_e \ge L+1Ne​≥L+1. In particular, for Ne=L+1N_e=L+1Ne​=L+1, the ground state is ferromagnetic with total spin sg=(Ne−2)/2s_g=(N_e-2)/2sg​=(Ne​−2)/2.
The problem of the ground state of the electronic system in the Hubbard model for U=∞ is discussed. The author investigates the normal (singlet or nonmagnetic) N state of the electronic system over the entire range of electron densities n⩽1. It is shown that the energy of the N state ɛ 0 (1) (n) in a one-particle approximation, such as (e.g.) the extended Hartree-Fock approximation, is lower than the energy of the saturated ferromagnetic FM state ɛ FM(n) for all n. The dynamic magnetic susceptibility is calculated in the random phase approximation, and it is shown that the N state is stable over the entire range of electron densities: The static susceptibility (ω=0) does not have a band singularity in the zero-wave vector limit q→0. A formally exact representation is obtained for the mass operator of the one-particle Green’s function, and an approximation of this operator is proposed: M k(E)⋍λF(E), where λ=n(1−n)/(1−n/2)z is the kinematic interaction parameter, z is the number of nearest neighbors, and F(E) is the total single-site Green’s function. For an elliptical density of states the integral equation for F(E) is solved exactly, ad it is shown that the spectral intensity rigorously satisfies the sum rule. The calculated energy of the strongly correlated N state ɛ 0(n)<ɛ FM(n) for all n, and in light of this relationship the author discusses the hypothesis that the ground state of the system is the normal (singlet) state in the thermodynamic limit. The electron distribution function at T=0 differs significantly from the Fermi step; it is “smeared” along the entire energy spectrum, and discontinuities do not occur in the region of the chemical potential m.
We show that the exact ground state for a class of extended Hubbard models including bond-charge, exchange, and pair-hopping terms, is the Yang ``\ensuremath{\eta}-paired'' state for any nonvanishing positive value of the pair-hopping amplitude, at least when the on-site Coulomb interaction is attractive enough and the remaining physical parameters satisfy a single constraint. The ground state is thus rigorously superconducting. Our result holds on a bipartite lattice in any dimension, at any band filling, and for arbitrary electron hopping. \textcopyright{} 1996 The American Physical Society.