Question
Description acceptable. Spins with this relationship are coupled in the Heisenberg and Ising models. For 10 points each:
[10m] Name this relationship that is indicated by placing indices in angle brackets below the summation notation in the Hamiltonians of the Heisenberg and Ising models.
ANSWER: they are nearest-neighbors [or they are adjacent; accept descriptions indicating two spins are next to each other]
[10h] A Heisenberg chain is the paradigmatic model of the “many-body” type of this phenomenon, which violates the eigenstate thermalization hypothesis. In a different type of this phenomenon, high disorder strength causes the electron wavefunction to decay exponentially.
ANSWER: localization [accept many-body localization; accept Anderson localization or strong localization; reject “weak localization” or “anti-localization” or “Mott localization”]
[10e] The entropy of this phenomenon scales with the subsystem area, rather than volume, in many-body localization states. Quantum states experiencing this phenomenon are correlated no matter how far apart they are.
ANSWER: quantum entanglement [or entangled or other word forms; accept entanglement entropy or entropy of entanglement]
Data
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total |
|---|---|---|---|---|---|
| Chicago A | Stanford A | 0 | 10 | 10 | 20 |
| Chicago C | Indiana A | 0 | 0 | 10 | 10 |
| Claremont A | Rutgers A | 0 | 0 | 10 | 10 |
| Columbia A | Minnesota A | 0 | 0 | 10 | 10 |
| Cornell A | Brown A | 10 | 10 | 10 | 30 |
| Duke A | Florida A | 0 | 0 | 10 | 10 |
| Florida B | Columbia B | 0 | 0 | 10 | 10 |
| Harvard A | Northwestern A | 0 | 0 | 10 | 10 |
| Illinois A | McGill A | 0 | 0 | 10 | 10 |
| Imperial A | Minnesota B | 0 | 0 | 10 | 10 |
| Iowa State A | Georgia Tech B | 0 | 0 | 10 | 10 |
| Johns Hopkins A | Purdue A | 0 | 0 | 10 | 10 |
| NYU A | Vanderbilt A | 0 | 0 | 10 | 10 |
| Ohio State A | Maryland A | 0 | 0 | 10 | 10 |
| Penn State A | South Carolina A | 0 | 0 | 10 | 10 |
| Rutgers B | Michigan A | 0 | 0 | 10 | 10 |
| Texas A | MIT A | 0 | 10 | 10 | 20 |
| Toronto A | North Carolina A | 0 | 0 | 10 | 10 |
| UC Berkeley A | Cornell B | 10 | 0 | 10 | 20 |
| UC Berkeley B | Houston A | 10 | 10 | 10 | 30 |
| Virginia A | Yale B | 10 | 0 | 10 | 20 |
| WUSTL A | Chicago B | 0 | 10 | 10 | 20 |
| WUSTL B | Penn A | 0 | 0 | 10 | 10 |
| Yale A | Georgia Tech A | 0 | 0 | 10 | 10 |