Discrete scale-invariant boson-fermion duality in one dimension
| Autor: | Satoshi Ohya |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Physical Review A. 105 |
| ISSN: | 2469-9934 2469-9926 |
| DOI: | 10.1103/physreva.105.033312 |
| Popis: | We introduce models of one-dimensional $n(\geq3)$-body problems that undergo phase transition from a continuous scale-invariant phase to a discrete scale-invariant phase. In this paper, we focus on identical spinless particles that interact only through two-body contacts. Without assuming any particular cluster-decomposition property, we first classify all possible scale-invariant two-body contact interactions that respect unitarity, permutation invariance, and translation invariance in one dimension. We then present a criterion for the breakdown of continuous scale invariance to discrete scale invariance. Under the assumption that the criterion is met, we solve the many-body Schr\"{o}dinger equation exactly; we obtain the exact $n$-body bound-state spectrum as well as the exact $n$-body S-matrix elements for arbitrary $n\geq3$, all of which enjoy discrete scale invariance or log-periodicity. Thanks to the boson-fermion duality, these results can be applied equally well to both bosons and fermions. Finally, we demonstrate how the criterion is met in the case of $n=3$; we determine the exact phase diagram for the scale-invariance breaking in the three-body problem of identical bosons and fermions. The zero-temperature transition from the unbroken phase to the broken phase is the Berezinskii-Kosterlitz-Thouless-like transition discussed in the literature. Comment: 15 pages, 6 eepic figures; typos corrected, references added, discussions improved |
| Databáze: | OpenAIRE |
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