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]
<Physics>