Related papers: Dynamical quantum phase transitions on random networks

Dynamical quantum phase transitions on random networks

URL: http://arxiv.org/abs/2503.04891v1
Date: Thu, 06 Mar 2025 19:00:01 GMT
Title: Dynamical quantum phase transitions on random networks
Authors: Tomohiro Hashizume, Felix Herbort, Joseph Tindall, Dieter Jaksch,
Abstract summary: We investigate two types of dynamical quantum phase transitions (DQPTs) in the transverse field Ising model on networks of size $N$.<n>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.<n>Our analysis suggests that this divergence arises from persistent non-trivial global many-body correlations absent in the $p=1$ limit.
Score: 0.0
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Abstract: We investigate two types of dynamical quantum phase transitions (DQPTs) in the transverse field Ising model on ensembles of Erd\H{o}s-R\'enyi 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.

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