Tomohiro Hashizume, Felix Herbort, Joseph Tindall and Dieter Jaksch
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⩽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 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
Cite as BibTeX
@article{Hashizume_2025,
doi = {10.1088/1367-2630/ade07b},
url = {https://dx.doi.org/10.1088/1367-2630/ade07b},
year = {2025},
month = {jun},
publisher = {IOP Publishing},
volume = {27},
number = {6},
pages = {064506},
author = {Hashizume, Tomohiro and Herbort, Felix and Tindall, Joseph and Jaksch, Dieter},
title = {Dynamical quantum phase transitions on random networks},
journal = {New Journal of Physics},
abstract = {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 (). 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 . 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.}
}