Temperley-Lieb Diagrams for Quantum Systems
Rachel Chen · Los Angeles, California
Fourth Place ($100,000) · Regeneron Science Talent Search · 2026
A diagrammatic representation of interacting quantum particle systems, using point-and-line diagrams to make the influence of magnetic fields visible in the structure itself.
Representation work is easy to undersell and hard to do. A notation that makes a property visible rather than computed is a genuine contribution, but only if you can show a question it makes easier.
- Temperley-Lieb algebra
- Diagrammatic representation
- Quantum spin system modelling
- Magnetic field dependence analysis
- A new representation earns its place by making some question easier — demonstrate that question
- Abstract work still needs a worked example; the example is how a judge checks that you understand it
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