Absence of small-world effects at the quantum level and stability of the quantum critical point
| Autor: | Ostilli, Massimo |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Phys. Rev. E 102, 052126 (2020) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1103/PhysRevE.102.052126 |
| Popis: | The small-world effect is a universal feature used to explain many different phenomena like percolation, diffusion, and consensus. Starting from any regular lattice of $N$ sites, the small-world effect can be attained by rewiring randomly an $\mathcal{O}(N)$ number of links or by superimposing an equivalent number of new links onto the system. In a classical system this procedure is known to change radically its critical point and behavior, the new system being always effectively mean-field. Here, we prove that at the quantum level the above scenario does not apply: when an $\mathcal{O}(N)$ number of new couplings are randomly superimposed onto a quantum Ising chain, its quantum critical point and behavior both remain unchanged. In other words, at zero temperature quantum fluctuations destroy any small-world effect. This exact result sheds new light on the significance of the quantum critical point as a thermodynamically stable feature of nature that has no analogous at the classical level and essentially prevents a naive application of network theory to quantum systems. The derivation is obtained by combining the quantum-classical mapping with a simple topological argument. Comment: 11 pages, 3 figures |
| Databáze: | arXiv |
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