Dynamical quantum phase transitions on random networks
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918068133822464 |
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| author | Hashizume, Tomohiro Herbort, Felix Tindall, Joseph Jaksch, Dieter |
| author_facet | Hashizume, Tomohiro Herbort, Felix Tindall, Joseph Jaksch, Dieter |
| contents | We investigate two types of dynamical quantum phase transitions (DQPTs) in the transverse field Ising model on ensembles of Erdős-Rényi networks of size $N$. These networks consist of vertices connected randomly with probability $p$ ($0<p\leq 1$). Using analytical derivations and numerical techniques, we compare the characteristics of the transitions for $p<1$ against the fully connected network ($p=1$). We analytically show that the overlap between the wave function after a quench and the wave function of the fully connected network after the same quench deviates by at most $\mathcal{O}(N^{-1/2})$. For a DQPT defined by an order parameter, the critical point remains unchanged for all $p$. For a DQPT defined by the rate function of the Loschmidt echo, we find that the rate function deviates from the $p=1$ limit near vanishing points of the overlap with the initial state, while the critical point remains independent for all $p$. Our analysis suggests that this divergence arises from persistent non-trivial global many-body correlations absent in the $p=1$ limit. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_04891 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamical quantum phase transitions on random networks Hashizume, Tomohiro Herbort, Felix Tindall, Joseph Jaksch, Dieter Quantum Physics We investigate two types of dynamical quantum phase transitions (DQPTs) in the transverse field Ising model on ensembles of Erdős-Rényi networks of size $N$. These networks consist of vertices connected randomly with probability $p$ ($0<p\leq 1$). Using analytical derivations and numerical techniques, we compare the characteristics of the transitions for $p<1$ against the fully connected network ($p=1$). We analytically show that the overlap between the wave function after a quench and the wave function of the fully connected network after the same quench deviates by at most $\mathcal{O}(N^{-1/2})$. For a DQPT defined by an order parameter, the critical point remains unchanged for all $p$. For a DQPT defined by the rate function of the Loschmidt echo, we find that the rate function deviates from the $p=1$ limit near vanishing points of the overlap with the initial state, while the critical point remains independent for all $p$. Our analysis suggests that this divergence arises from persistent non-trivial global many-body correlations absent in the $p=1$ limit. |
| title | Dynamical quantum phase transitions on random networks |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2503.04891 |