# A report on Hubbard model

Approximate model used, especially in solid-state physics, to describe the transition between conducting and insulating systems.

- Hubbard model9 related topics with Alpha

## Mott insulator

2 linksMott insulators are a class of materials that are expected to conduct electricity according to conventional band theories, but turn out to be insulators (particularly at low temperatures).

Mott insulators are a class of materials that are expected to conduct electricity according to conventional band theories, but turn out to be insulators (particularly at low temperatures).

One of the simplest models that can capture Mott transition is the Hubbard model.

## Electronic band structure

3 linksIn solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands).

In solid-state physics, the electronic band structure (or simply band structure) of a solid describes the range of energy levels that electrons may have within it, as well as the ranges of energy that they may not have (called band gaps or forbidden bands).

The Hubbard model is an approximate theory that can include these interactions.

## Dynamical mean-field theory

2 linksMethod to determine the electronic structure of strongly correlated materials.

Method to determine the electronic structure of strongly correlated materials.

Likewise, DMFT maps a lattice problem (e.g. the Hubbard model) onto a single-site problem.

## Bose–Hubbard model

0 linksThe Bose–Hubbard model gives a description of the physics of interacting spinless bosons on a lattice.

The Bose–Hubbard model gives a description of the physics of interacting spinless bosons on a lattice.

It is closely related to the Hubbard model which originated in solid-state physics as an approximate description of superconducting systems and the motion of electrons between the atoms of a crystalline solid.

## John Hubbard (physicist)

0 linksJohn Hubbard (27 October 1931 – 27 November 1980) was a British physicist, best known for the Hubbard model for interacting electrons, the Hubbard–Stratonovich transformation, and the Hubbard approximations.

## Tight binding

1 linksApproach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site.

Approach to the calculation of electronic band structure using an approximate set of wave functions based upon superposition of wave functions for isolated atoms located at each atomic site.

Modern explanations of electronic structure like t-J model and Hubbard model are based on tight binding model.

## Elliott H. Lieb

0 linksAmerican mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, condensed matter theory, and functional analysis.

American mathematical physicist and professor of mathematics and physics at Princeton University who specializes in statistical mechanics, condensed matter theory, and functional analysis.

In particular, his scientific works pertain to quantum and classical many-body problem, atomic structure, the stability of matter, functional inequalities, the theory of magnetism, and the Hubbard model.

## Bethe ansatz

0 linksAnsatz method for finding the exact wavefunctions of certain one-dimensional quantum many-body models.

Ansatz method for finding the exact wavefunctions of certain one-dimensional quantum many-body models.

Since then the method has been extended to other models in one dimension: the (anisotropic) Heisenberg chain (XXZ model), the Lieb-Liniger interacting Bose gas, the Hubbard model, the Kondo model, the Anderson impurity model, the Richardson model etc.

## Numerical sign problem

0 linksProblem of numerically evaluating the integral of a highly oscillatory function of a large number of variables.

Problem of numerically evaluating the integral of a highly oscillatory function of a large number of variables.

Condensed matter physics — It prevents the numerical solution of systems with a high density of strongly correlated electrons, such as the Hubbard model.