An exactly solvable many-body problem in one dimension and the short-range Dyson model. (English) Zbl 1059.81651
Summary: For \(N\) impenetrable particles in one dimension with upto next-to-nearest neighbours interaction, we obtain the exact ground state. We establish a mapping between these \(N\)-body problems and the short-range Dyson model introduced recently to model intermediate spectral statistics. We prove the absence of long-range order and off-diagonal long-range order in the corresponding many-body theory.
MSC:
| 81V70 | Many-body theory; quantum Hall effect |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
| 82B10 | Quantum equilibrium statistical mechanics (general) |
| 82B23 | Exactly solvable models; Bethe ansatz |
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