Su–Schrieffer–Heeger model¶

In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features.

Version: v1 · 2026-09-28 · History
Domain-specific #: 12397
Domain group: Natural Sciences
Origin domain: Physics
Subdomains: Condensed Matter Physics, Topological Phases → Physics

Core Idea¶

Su–Schrieffer–Heeger model is treated here as the recurring natural_sciences_engineering_health identity summarized by this source-grounded definition: In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features.

In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features. It was devised by Wu-Pei Su, John Robert Schrieffer, and Alan J. Heeger in 1979, to describe the increase of electrical conductivity of polyacetylene polymer chain when doped, based on the existence of solitonic defects.

It is a quantum mechanical tight binding approach, that describes the hopping of spinless electrons in a chain with two alternating types of bonds. Electrons in a given site can only hop to adjacent sites. Depending on the ratio between the hopping energies of the two possible bonds, the system can be either in metallic phase (conductive) or in an insulating phase.

For Su–Schrieffer–Heeger model, the abstraction is narrower than the article's general subject matter: a positive case must preserve In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features. Retaining only the name, a familiar example, or a downstream effect is insufficient. The specialist roles and tests remain anchored in natural_sciences_engineering_health, which is why this identity is domain-specific rather than prime.

Structural Signature¶

Sig role-phrases:

Defining carrier — In this configuration each electron can either hop inside the unit cell or hop to an adjacent cell through nearest neighbor sites.
Constitutive relation — The dispersion relation for the bulk can be obtained through a Fourier transform.
Operating condition — Taking periodic boundary conditions |N+1,X\rangle=|1,X\rangle , where X=A,B , we pass to k-space by doing.
Recognition evidence — This difference in topology means that one cannot pass from an insulating phase to another without closing the gap (passing by the metallic phase).
Admissible variation — By plotting the spectrum as a function of v for a fixed value of w , the spectrum is divided into two insulating regions divided by the metallic intersection at w=v .
Characteristic consequence — The bulk case allows to predict which insulating region would present edge states, depending on the value of the winding number in the bulk case.
Failure boundary — It was devised by Wu-Pei Su, John Robert Schrieffer, and Alan J.

What It Is Not¶

Not the whole field of natural_sciences_engineering_health. The node requires the specific identity stated by In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features.
Not an over-broad reading. Nevertheless, not all properties of the system are symmetrical, for example the eigenvectors are very different under swap of v\leftrightarrow w .
Not an over-broad reading. showing that the two insulating phases, v>w and v , are topologically different (small changes in v and w change A_-(k) but not g over the Brillouin zone).
Not an over-broad reading. The eigenenergies are symmetrical under swap of v\leftrightarrow w , and the dispersion relation is mostly gapped (insulator) except when v=w (metal).
Not automatically Scheutjens–Fleer theory. Retrieval proximity does not establish equivalence; the two identities must be compared by carrier, operation, and failure boundary.

Scope of Application¶

Su–Schrieffer–Heeger model applies literally inside natural_sciences_engineering_health wherever the source-defined carrier and relation can be established. Its documented habitats include:

Intermediate values. By plotting the eigenstates of the finite chain as function of position, one can show that there are two distinct kinds of states.
Intermediate values. For non-zero eigenenergies, the corresponding wavefunctions would be delocalized all along the chain while the zero energy eigenstates would portray localized amplitudes at the edge sites.
Intermediate values. By plotting the spectrum as a function of v for a fixed value of w , the spectrum is divided into two insulating regions divided by the metallic intersection at w=v .
Correspondence between finite and bulk solutions. The bulk case allows to predict which insulating region would present edge states, depending on the value of the winding number in the bulk case.
Documented setting. For the finite chain, there exists an insulating phase that is topologically non-trivial and allows for the existence of edge states that are localized at the boundaries.
Description. The model describes a half-filled one-dimensional lattice, with two sites per unit cell, A and B, which correspond to a single electron per unit cell.

Outside natural_sciences_engineering_health, the name should be retained only when these same operational conditions survive; otherwise the comparison belongs to the broader parent Theory or should be marked as analogy.

Clarity¶

A clear use of Su–Schrieffer–Heeger model names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features. The strongest recognition evidence in the frozen account is: This difference in topology means that one cannot pass from an insulating phase to another without closing the gap (passing by the metallic phase). A report should distinguish that evidence from a proxy, consequence, or common implementation. It should also state the qualification Nevertheless, not all properties of the system are symmetrical, for example the eigenvectors are very different under swap of v\leftrightarrow w . so that a reader can reproduce the classification rather than infer it from topical resemblance.

Manages Complexity¶

Su–Schrieffer–Heeger model compresses multiple natural_sciences_engineering_health details into a stable diagnostic relation. The source shows both the central mechanism—the dispersion relation for the bulk can be obtained through a Fourier transform.—and the practical consequence—the bulk case allows to predict which insulating region would present edge states, depending on the value of the winding number in the bulk case. This compression makes cases comparable while leaving parameters, conventions, exceptions, and evidential quality explicit. It is lossy by design: local history and implementation details may be omitted only when they do not alter the defining relation.

Abstract Reasoning¶

Type the carrier. Identify the natural_sciences_engineering_health entities to which the claim applies.
State the relation. Use the source-grounded identity: In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features.
Check operation and conditions. Taking periodic boundary conditions |N+1,X\rangle=|1,X\rangle , where X=A,B , we pass to k-space by doing.
Demand recognition evidence. This difference in topology means that one cannot pass from an insulating phase to another without closing the gap (passing by the metallic phase).
Test variation. Change an implementation or setting while preserving by plotting the spectrum as a function of v for a fixed value of w , the spectrum is divided into two insulating regions divided by the metallic intersection at w=v .
Run the collapse test. Remove the defining operation; if the label still seems equally apt, only a topic or correlate was retained.
Reduce cautiously. When the specialist conditions cannot be carried, route the residual comparison to Theory.

Knowledge Transfer¶

Within the home domain. Knowledge about Su–Schrieffer–Heeger model transfers literally when a new case preserves the same carrier type, relation, and recognition test. By plotting the eigenstates of the finite chain as function of position, one can show that there are two distinct kinds of states. For non-zero eigenenergies, the corresponding wavefunctions would be delocalized all along the chain while the zero energy eigenstates would portray localized amplitudes at the edge sites.

Beyond the home domain. No canonical parent is asserted for Su–Schrieffer–Heeger model. An outside case receives the specialist name only when the same typed roles and rejection conditions can be filled literally; otherwise the comparison remains an analogy pending later graph densification.

Examples¶

Canonical¶

Nevertheless, not all properties of the system are symmetrical, for example the eigenvectors are very different under swap of v\leftrightarrow w . This case is canonical because it supplies a concrete carrier and lets the defining relation be checked rather than merely named.

Mapped back: carrier → the entities in the documented case; operation → In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features; recognition evidence → This difference in topology means that one cannot pass from an insulating phase to another without closing the gap (passing by the metallic phase)

Applied / In Practice¶

It is much harder to diagonalize the Hamiltonian analytically in the finite case due to the lack of translational symmetry. The applied case shows how the identity is used under a second setting or qualification while keeping the same operative relation.

Mapped back: changed setting → Finite chain solution and edge states; invariant → In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features; boundary → the case exits the class when nevertheless, not all properties of the system are symmetrical, for example the eigenvectors are very different under swap of v\leftrightarrow w

Structural Tensions¶

T1 — Stable identity versus admissible variation. Nevertheless, not all properties of the system are symmetrical, for example the eigenvectors are very different under swap of v\leftrightarrow w . The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Which changes preserve the defining relation, and which replace it?

T2 — Recognition versus proxy. showing that the two insulating phases, v>w and v , are topologically different (small changes in v and w change A_-(k) but not g over the Brillouin zone). The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the cited evidence establish the identity or only a correlated sign?

T3 — Definition versus implementation. The eigenenergies are symmetrical under swap of v\leftrightarrow w , and the dispersion relation is mostly gapped (insulator) except when v=w (metal). The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Is the observed implementation constitutive, optional, or merely common?

T4 — Scope versus overextension. integrated over the Brillouin zone k\in{-\pi,\pi} , produces different winding numbers. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Can every claimed application fill the same typed roles without metaphor?

T5 — Transfer versus domain accent. In this configuration each electron can either hop inside the unit cell or hop to an adjacent cell through nearest neighbor sites. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: Does the receiving case instantiate Su–Schrieffer–Heeger model literally, co-instantiate Theory, or only resemble it?

T6 — Autonomy versus reduction. The dispersion relation for the bulk can be obtained through a Fourier transform. The tension matters because emphasizing only one side either dissolves the identity or overstates what the evidence and domain conventions warrant.

Diagnostic: What does Su–Schrieffer–Heeger model distinguish that the broader parent Theory leaves together?

Structural–Framed Character¶

Su–Schrieffer–Heeger model is structural-leaning. Its structural side is the repeatable organization summarized by In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features. Its framed side is the natural_sciences_engineering_health vocabulary that fixes the carrier, evidence, exceptions, and admissible transformations.

Evaluative weight: the identity can be stated descriptively even when applications carry practical stakes. Human-practice dependence: the source-grounded carrier determines whether the relation exists independently or is constituted by a practice. Institutional origin: disciplinary conventions stabilize the name and test. Vocabulary portability: Taking periodic boundary conditions |N+1,X\rangle=|1,X\rangle , where X=A,B , we pass to k-space by doing. Import versus recognition: literal transfer requires the same mechanism; shape alone is analogy.

Its portable skeleton is Theory. Its character: a recurring specialist identity whose thin organization can be abstracted, while its operational meaning remains domain-bound.

Structural Core vs. Domain Accent¶

What is skeletal. In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features. The stable skeleton is the typed relation expressed in that definition and the entry's recognition and collapse tests. The source identifies these operative conditions: In this configuration each electron can either hop inside the unit cell or hop to an adjacent cell through nearest neighbor sites. The dispersion relation for the bulk can be obtained through a Fourier transform. It further constrains recognition and variation through: Taking periodic boundary conditions |N+1,X\rangle=|1,X\rangle , where X=A,B , we pass to k-space by doing. This difference in topology means that one cannot pass from an insulating phase to another without closing the gap (passing by the metallic phase).

What is domain-bound. natural sciences engineering health supplies the operative entities, technical vocabulary, warrants, and exceptions that make Su–Schrieffer–Heeger model literal. Its documented scope includes the condition that By plotting the eigenstates of the finite chain as function of position, one can show that there are two distinct kinds of states. Another bounded application condition is that For non-zero eigenenergies, the corresponding wavefunctions would be delocalized all along the chain while the zero energy eigenstates would portray localized amplitudes at the edge sites. These are not decorative examples; they determine which carrier and evidence can fill the abstraction's roles.

Why no parent is asserted. Removing those specialist details does not currently yield one live catalog node that is a necessary genus for every instance. The entry is therefore approved as unparented rather than attached by topical resemblance. Its collapse evidence remains specific—By plotting the spectrum as a function of v for a fixed value of w , the spectrum is divided into two insulating regions divided by the metallic intersection at w=v .—and future graph densification may discover a defensible relation only if it preserves that boundary.

This entry is a kind of Lattice Model (Physics).

Approved unparented node. No current live node supplies a defensible necessary genus or structural prerequisite for Su–Schrieffer–Heeger model. The reviewed identity is: In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features. The accelerated suggestion was declined because topical or lexical similarity does not establish hierarchy; the node is admitted without a parent pending later graph densification.
Related reasoning operations. Evidence, representation, comparison, classification, transformation, or evaluation may participate in particular cases, but participation does not make any one of them a necessary parent of every instance.

Relationships to Other Abstractions¶

Current abstraction Su–Schrieffer–Heeger model Domain-specific

Parents (1) — more general patterns this builds on

Su–Schrieffer–Heeger model is a kind of Lattice Model (Physics) Domain-specific

The SSH model is a one-dimensional lattice model with alternating couplings and a topological band structure.

Hierarchy path (1) — routes to 1 parentless root

Su–Schrieffer–Heeger model → Lattice Model (Physics) → Physical-System Model → Representation → Abstraction

Neighborhood in Abstraction Space¶

Su–Schrieffer–Heeger model sits in a crowded region of the domain-specific corpus (33^rd percentile for distinctiveness): several abstractions share nearly its structure, so a description that fits it tends to fit its neighbors too.

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

Nearest neighbors

Crystal momentum — 0.90
Dephasing rate SP formula — 0.89
Hubbard model — 0.88
Single Vegetative Obstruction Model — 0.88
Mehler Kernel — 0.88

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

Not to Be Confused With¶

Theory. The parent omits the specialist differentia. Tell: Can the case establish In condensed matter physics, the Su–Schrieffer–Heeger (SSH) model or SSH chain is a one-dimensional lattice model that presents topological features?
Scheutjens–Fleer theory. A lattice self-consistent-field framework for computing equilibrium segment-density profiles of polymers near interfaces under incompressibility and mean-field interaction assumptions. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Frenkel–Kontorova model. A model of elastically coupled particles in a periodic substrate potential that captures competition between a preferred spacing and an imposed lattice. Tell: Which entry's carrier, operation, and failure condition are satisfied?
Particle in a one-dimensional lattice. The quantum model of a particle moving in a spatially periodic one-dimensional potential, whose stationary states have Bloch form and organize into energy bands separated by gaps. Tell: Which entry's carrier, operation, and failure condition are satisfied?
A measurement, proxy, or consequence. Those may provide evidence without being the identity. Tell: Would Su–Schrieffer–Heeger model remain present if the detector or downstream effect changed?
A metaphorical analogue. A similar shape outside natural_sciences_engineering_health lacks the specialist mechanism. Tell: Do the native roles transfer literally, or only the parent Theory?

References¶

Frozen Wikipedia discovery revision: https://en.wikipedia.org/wiki/Su%E2%80%93Schrieffer%E2%80%93Heeger_model (revision 1369621536).
Preserved source candidate: https://link.springer.com/10.1007/s12045-020-0995-x
Preserved source candidate: https://link.aps.org/doi/10.1103/PhysRevLett.42.1698

The frozen Wikipedia revision is discovery provenance. The retained source set was reviewed for identity, formal or operational relation, and scope. The encyclopedia's structural synthesis is bounded to those claims; a thin authority surface is recorded as a nonblocking source-strengthening repair rather than concealed.