Determining the validity of cumulant expansions for central spin models
| Autor: | Fowler-Wright, Piper, Arnardóttir, Kristín B., Kirton, Peter, Lovett, Brendon W., Keeling, Jonathan |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Phys. Rev. Research 5, 033148 (2023) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevResearch.5.033148 |
| Popis: | For a model with many-to-one connectivity it is widely expected that mean-field theory captures the exact many-particle $N\to\infty$ limit, and that higher-order cumulant expansions of the Heisenberg equations converge to this same limit whilst providing improved approximations at finite $N$. Here we show that this is in fact not always the case. Instead, whether mean-field theory correctly describes the large-$N$ limit depends on how the model parameters scale with $N$, and the convergence of cumulant expansions may be non-uniform across even and odd orders. Further, even when a higher-order cumulant expansion does recover the correct limit, the error is not monotonic with $N$ and may exceed that of mean-field theory. Comment: 9 pages, 6 figures, final published version |
| Databáze: | arXiv |
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