Hubbard model

The Hubbard model is a simplified model used to describe the transition between conducting and insulating systems.

Version

v1 · 2026-09-28 · History

Domain-specific #

9917

Domain group

Natural Sciences

Origin domain

Physics

Subdomains

Condensed Matter Physics, Strongly Correlated Electrons → Physics

Core Idea

Hubbard model is treated here as the recurring condensed-matter physics identity summarized by this source-grounded definition: The Hubbard model is a simplified model used to describe the transition between conducting and insulating systems. The Hubbard model is a simplified model used to describe the transition between conducting and insulating systems. It is particularly useful in solid-state physics. The model is named after John Hubbard. The Hubbard model states that each electron experiences competing forces: one pushes it to tunnel to neighboring atoms, while the other pushes it away from its neighbors.

Scope of Application

• Narrow energy band theory. This coupling allows states associated with each lattice site to hybridize, and the eigenstates of such a crystalline system are Bloch's functions, with the energy levels divided into separated energy bands.

• Numerical treatment. DMFT allows one to compute the local Green's function of the Hubbard model for a given U and a given temperature.

• Simulator. A "backwards" stacking regime allows the creation of a Chern insulator via the anomalous quantum Hall effect (with the edges of the device acting as a conductor while the interior acted.

• Narrow energy band theory. When the Hubbard model is used to describe electron systems, these interactions are expected to be repulsive, stemming from the screened Coulomb interaction.

• Narrow energy band theory. For example, it has been used to describe metal oxides as they are heated, where the corresponding increase in nearest-neighbor spacing reduces the hopping integral to the point where the on-site.

Clarity

A clear use of Hubbard model names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is The Hubbard model is a simplified model used to describe the transition between conducting and insulating systems.

Manages Complexity

Hubbard model compresses multiple condensed-matter physics details into a stable diagnostic relation. The source shows both the central mechanism—this coupling allows states associated with each lattice site to hybridize, and the eigenstates of such a crystalline system are Bloch's functions, with the energy levels divided into separated energy bands.—and the practical consequence—the first term describes the kinetic energy of the system, parameterized by the hopping integral, t.

Abstract Reasoning

1. Type the carrier. Identify the condensed-matter physics entities to which the claim applies.
2. State the relation. Use the source-grounded identity: The Hubbard model is a simplified model used to describe the transition between conducting and insulating systems.
3. Check operation and conditions. The width of the bands depends upon the value of the hopping integral.
4. Demand recognition evidence.

Knowledge Transfer

Within the home domain. Knowledge about Hubbard model transfers literally when a new case preserves the same carrier type, relation, and recognition test. This coupling allows states associated with each lattice site to hybridize, and the eigenstates of such a crystalline system are Bloch's functions, with the energy levels divided into separated energy bands. DMFT allows one to compute the local Green's function of the Hubbard model for a given U and a given temperature. Beyond the home domain. Transfer the broader Theory relation when the condensed-matter physics-specific differentia cannot be filled.

Relationships to Other Abstractions

Current abstraction Hubbard model Domain-specific

Parents (1) — more general patterns this builds on

• Hubbard model is a kind of Theory Prime

  Hubbard model is a strict kind of Theory: The Hubbard model is a simplified model used to describe the transition between conducting and insulating systems.

Hierarchy paths (2) — routes to 2 parentless roots

• Hubbard model → Theory → Formalization → Representation → Abstraction

Show alternative path (1)

Neighborhood in Abstraction Space

Hubbard model sits in a moderately populated region (52^nd percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Condensed Matter & Physical Chemistry Models (26 abstractions)

Nearest neighbors

• Su–Schrieffer–Heeger model — 0.88
• Crystal momentum — 0.88
• Heavy-Fermion Material — 0.86
• Elliott formula — 0.85
• Glauber dynamics — 0.85

Computed from structural-signature embeddings · 2026-10-08