Pairwise entanglement networks as a probe into non-equilibirum quantum dynamics

Abstract

Following a sudden change of system parameters known as a quantum quench, the state of a quantum system can exhibit out-of-equilibrium dynamics. When the quench is across a critical point, a dynamical phase transition can occur, indicated by non-analytic behavior in a quantity known as Loschmidt echo. However, measuring the Loschmidt echo requires measurement of the entire quantum state, which is experimentally challenging, even for a moderate system size of a few tens of quantum particles. To address the challenge of detecting dynamical phase transitions, we investigate the possibility of using only information from two-body reduced states of a quantum many-body system for identifying dynamical phase transitions. These two-body reduced states allow us to calculate a network of different pairwise entanglement measures, including connected correlations, concurrence, and mutual information. As the measurement of all two-body reduced states only requires resources quadratic in system size, obtaining pairwise networks of these entanglement measures is experimentally practical. Upon attaining the pairwise networks, we directly examine the weighted adjacency matrices using network science and spectral graph analysis. Our results show that concurrence, an entanglement monotone, oscillates in phase with the rate function. As an example of our procedure, we consider a long-range transverse field Ising model with power-law interactions in the coupling strength. We further show that our methods may provide a considerably more efficient method for probing dynamical phase transitions in a large quantum many-body system. This work also paves the way for characterizing the role of pairwise entanglement in identifying critical phenomena.