non-Abelian Berry connection
E911212
concept in geometric phase theory
concept in quantum mechanics
gauge field
geometric connection
matrix-valued Berry connection
The non-Abelian Berry connection is a gauge-theoretic generalization of the Berry phase that describes how degenerate quantum states transform under adiabatic evolution, leading to matrix-valued geometric phases and phenomena such as the Yang monopole.
All labels observed (1)
| Label | Occurrences |
|---|---|
| non-Abelian Berry connection canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T11205517 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: non-Abelian Berry connection Context triple: [Yang monopole, relatedTo, non-Abelian Berry connection]
-
A.
Aharonov–Casher effect
The Aharonov–Casher effect is a quantum mechanical phenomenon in which a neutral particle with a magnetic moment acquires a measurable phase shift when moving around a line of electric charge, illustrating the significance of electromagnetic potentials.
-
B.
Peierls bracket
The Peierls bracket is a covariant generalization of the Poisson bracket used in quantum field theory and classical field theory to define commutation relations in a way that respects spacetime causality.
-
C.
Aharonov–Bohm effect
The Aharonov–Bohm effect is a quantum mechanical phenomenon in which charged particles are influenced by electromagnetic potentials in regions where the classical electromagnetic fields are zero, revealing the physical significance of potentials in quantum theory.
-
D.
Peierls substitution
Peierls substitution is a quantum mechanical method for incorporating the effects of an external electromagnetic field into the momentum of charged particles in lattice or solid-state systems.
-
E.
Kubo-Greenwood formula for conductivity
The Kubo-Greenwood formula for conductivity is a quantum-mechanical expression that relates a material’s electrical conductivity to its electronic states and transition probabilities, widely used to compute transport properties from first-principles calculations.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: non-Abelian Berry connection Target entity description: The non-Abelian Berry connection is a gauge-theoretic generalization of the Berry phase that describes how degenerate quantum states transform under adiabatic evolution, leading to matrix-valued geometric phases and phenomena such as the Yang monopole.
-
A.
Aharonov–Casher effect
The Aharonov–Casher effect is a quantum mechanical phenomenon in which a neutral particle with a magnetic moment acquires a measurable phase shift when moving around a line of electric charge, illustrating the significance of electromagnetic potentials.
-
B.
Peierls bracket
The Peierls bracket is a covariant generalization of the Poisson bracket used in quantum field theory and classical field theory to define commutation relations in a way that respects spacetime causality.
-
C.
Aharonov–Bohm effect
The Aharonov–Bohm effect is a quantum mechanical phenomenon in which charged particles are influenced by electromagnetic potentials in regions where the classical electromagnetic fields are zero, revealing the physical significance of potentials in quantum theory.
-
D.
Peierls substitution
Peierls substitution is a quantum mechanical method for incorporating the effects of an external electromagnetic field into the momentum of charged particles in lattice or solid-state systems.
-
E.
Kubo-Greenwood formula for conductivity
The Kubo-Greenwood formula for conductivity is a quantum-mechanical expression that relates a material’s electrical conductivity to its electronic states and transition probabilities, widely used to compute transport properties from first-principles calculations.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
concept in geometric phase theory
ⓘ
concept in quantum mechanics ⓘ gauge field ⓘ geometric connection ⓘ matrix-valued Berry connection ⓘ |
| appliesTo | degenerate quantum states ⓘ |
| associatedWith |
degenerate eigenspaces
ⓘ
vector bundles of degenerate states ⓘ |
| captures |
non-Abelian holonomy
ⓘ
path-dependent unitary transformations ⓘ |
| contrastsWith |
Abelian Berry connection
ⓘ
linked to:
Berry phase
|
| definedFor | families of Hamiltonians with degeneracies ⓘ |
| definedFrom | basis of instantaneous degenerate eigenstates ⓘ |
| definedOn | parameter space of a Hamiltonian ⓘ |
| describes |
adiabatic evolution of degenerate subspaces
ⓘ
holonomy in parameter space ⓘ non-Abelian geometric phases ⓘ parallel transport of degenerate eigenstates ⓘ |
| enables |
description of Yang monopole
ⓘ
matrix-valued geometric phases ⓘ |
| gaugeGroup |
U(N)
ⓘ
linked to:
U(n)
unitary group ⓘ |
| generalizationOf |
Abelian Berry phase
ⓘ
linked to:
Berry phase
Berry connection ⓘ |
| hasMathematicalForm | matrix-valued one-form on parameter space ⓘ |
| hasProperty |
adiabatic
ⓘ
gauge-dependent ⓘ geometric ⓘ matrix-valued ⓘ non-commutative ⓘ |
| introducedInContextOf | adiabatic theorem ⓘ |
| relatedTo |
Berry curvature
ⓘ
Wilczek–Zee phase ⓘ
linked to:
Berry phase
Yang monopole ⓘ fiber bundles ⓘ gauge theory ⓘ holonomy group ⓘ non-Abelian Berry curvature ⓘ |
| requires | degeneracy of energy levels ⓘ |
| takesValuesIn |
Lie algebra of a unitary group
ⓘ
u(N) ⓘ |
| transformsUnder | non-Abelian gauge transformations ⓘ |
| usedIn |
adiabatic quantum computation
ⓘ
holonomic quantum computation ⓘ non-Abelian anyons ⓘ quantum Hall systems ⓘ topological insulators ⓘ topological phases of matter ⓘ topological superconductors ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: non-Abelian Berry connection Description of subject: The non-Abelian Berry connection is a gauge-theoretic generalization of the Berry phase that describes how degenerate quantum states transform under adiabatic evolution, leading to matrix-valued geometric phases and phenomena such as the Yang monopole.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.