REVIEW ARTICLE: The Hubbard model - an introduction and selected rigorous results

@article{Tasaki1998REVIEWAT,
  title={REVIEW ARTICLE: The Hubbard model - an introduction and selected rigorous results},
  author={Hal Tasaki},
  journal={Journal of Physics: Condensed Matter},
  year={1998}
}
  • H. Tasaki
  • Published 25 May 1998
  • Physics
  • Journal of Physics: Condensed Matter
The Hubbard model is a `highly oversimplified model' for electrons in a solid which interact with each other through extremely short-ranged repulsive (Coulomb) interaction. The Hamiltonian of the Hubbard model consists of two parts: which describes quantum mechanical hopping of electrons, and which describes non-linear repulsive interaction. Either or alone is easy to analyse, and does not favour any specific order. But their sum is believed to exhibit various non-trivial phenomena including… 
Ferromagnetism in the Hubbard Model: A Constructive Approach
AbstractIt is believed that strong ferromagnetic orders in some solids are generated by subtle interplay between quantum many-body effects and spin-independent Coulomb interactions between electrons.
The Hubbard model within the equations of motion approach
The Hubbard model plays a special role in condensed matter theory as it is considered to be the simplest Hamiltonian model one can write in order to describe anomalous physical properties of some
Frustrated quantum Heisenberg antiferromagnets at high magnetic fields: Beyond the flat-band scenario
We consider the spin-1/2 antiferromagnetic Heisenberg model on three frustrated lattices (the diamond chain, the dimer-plaquette chain, and the two-dimensional square-kagome lattice) with almost
Complete spectrum of the infinite-U Hubbard ring using group theory.
TLDR
The proposed group theoretical strategy to solve the infinite-U Hubbard problem for N-1 electrons is easily generalized to the case of arbitrary electron count L, by analyzing the permutation group CL and all its subgroups.
The Study of Strongly Correlated Electronic Systems using Dynamical Mean field Theory
The physics of strongly correlated electronic systems has attracted much attention because of its unique and distinct properties like Mott metal-to-insulator transition, giant magneto-resistance,
Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
In this review we recapitulate the basic features of the flat-band spin systems and briefly summarize earlier studies in the field. Main emphasis is made on recent developments which include results
Hubbard model on the honeycomb lattice: From static and dynamical mean-field theories to lattice quantum Monte Carlo simulations
We study the one-band Hubbard model on the honeycomb lattice using a combination of quantum Monte Carlo (QMC) simulations and static as well as dynamical mean-field theory (DMFT). This model is known
Universal thermodynamics of an SU(N) Fermi-Hubbard model
The SU(2) symmetric Fermi-Hubbard model (FHM) plays an essential role in strongly correlated fermionic many-body systems. In the one particle per site and strongly interacting limit ${U/t \gg 1}$, it
Low-temperature properties of the Hubbard model on highly frustrated one-dimensional lattices
We consider the repulsive Hubbard model on three highly frustrated one-dimensional lattices---sawtooth chain and two kagom\'e chains---with completely dispersionless (flat) lowest single-electron
...
...

References

SHOWING 1-10 OF 117 REFERENCES
Stability of ferromagnetism in Hubbard models with nearly flat bands
Whether spin-independent Coulomb interaction in an electron system can be the origin of ferromagnetism has been an open problem for a long time. Recently, a “constructive” approach to this problem
Non-perturbative approaches to magnetism in strongly correlated electron systems
The microscopic basis for the stability of itinerant ferromagnetism in correlated electron systems is examined. To this end several routes to ferromagnetism are explored, using both rigorous methods
Ferromagnetism in the Hubbard model
Whether spin-independent Coulomb interaction can be the origin of a realistic ferromagnetism in an itinerant electron system has been an open problem for a long time. Here we study a class of Hubbard
FROM NAGAOKA'S FERROMAGNETISM TO FLAT-BAND FERROMAGNETISM AND BEYOND : AN INTRODUCTION TO FERROMAGNETISM IN THE HUBBARD MODEL
This is a self-contained review about ferromagnetism in the Hubbard model, which should be accessible to readers with various backgrounds who are new to the field. We describe Nagaoka's
Uniform density theorem for the Hubbard model
A general class of hopping models on a finite bipartite lattice is considered, including the Hubbard model and the Falicov–Kimball model. For the half‐filled band, the single‐particle density matrix
Symmetry breaking and finite-size effects in quantum many-body systems
We consider a quantum many-body system on a lattice which exhibits a spontaneous symmetry breaking in its infinite-volume ground states, but in which the corresponding order operator does not commute
Exchange in solid 3He and the Heisenberg Hamiltonian
The nuclear spins in solid 3He are coupled to one another as a result of the Pauli exclusion principle. The exchange energy is so small that the Pauli principle can be treated rigourously as a
Exact ground states for the Hubbard model on the Kagome lattice
The author gives a complete and rigorous description of the ground states of the Hubbard model on the Kagome lattice for electron densities n>or=5/3 and U>0. If 11/6>n>or=5/3 the system shows a
Ferromagnetism in Hubbard models.
  • Tasaki
  • Physics
    Physical review letters
  • 1995
We present the first rigorous examples of non-singular Hubbard models which exhibit ferromagnetism at zero temperature. The models are defined in arbitrary dimensions, and are characterized by
Failure of saturated ferromagnetism for the Hubbard model with two holes
We consider the Hubbard model on a finite set of sites with nonpositive hopping matrix elements and infinitely strong on-site repulsion. Nagaoka's theorem states that in this model the relative
...
...