Entanglement growth in quench dynamics with variable range interactions

By J. Schachenmayer, B. Lanyon, C. F. Roos, Andrew J. Daley. 2013

171 citations recorded by the source corpus.

Studying entanglement growth in quantum dynamics provides both insight into the underlying microscopic processes and information about the complexity of the quantum states, which is related to the efficiency of simulations on classical computers. Recently, experiments with trapped ions, polar molecules, and Rydberg excitations have provided new opportunities to observe dynamics with long-range interactions. We explore nonequilibrium coherent dynamics after a quantum quench in such systems, identifying qualitatively different behavior as the exponent of algebraically decaying spin-spin interactions in a transverse Ising chain is varied. Computing the build-up of bipartite entanglement as well as mutual information between distant spins, we identify linear growth of entanglement entropy corresponding to propagation of quasiparticles for shorter range interactions, with the maximum rate of growth occurring when the Hamiltonian parameters match those for the quantum phase transition. Counter-intuitively, the growth of bipartite entanglement for long-range interactions is only logarithmic for most regimes, i.e., substantially slower than for shorter range interactions. Experiments with trapped ions allow for the realization of this system with a tunable interaction range, and we show that the different phenomena are robust for finite system sizes and in the presence of noise. These results can act as a direct guide for the generation of large-scale entanglement in such experiments, towards a regime where the entanglement growth can render existing classical simulations inefficient.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/4ffe196b20ac7d38e0e91170bcfdae79d3ba6a52

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Citations in the corpus

Efficient tomography of a quantum many-body system (2016, background): “That the amount of entanglement in the simulator is growing in time can be seen from the inset in figure 3a: the half-chain entropies of the certified MPSs |ψ(3)c〉 are seen to grow as expected for a sudden quench [27].”
Long-range Ising and Kitaev models: phases, correlations and edge modes (2015, background): “Recent experiments have led to the observation of instances of interaction-induced frustration [18], nonlocal propagation of correlations [19–23] and entanglement in a quantum many-body system [16, 24].”
Quantum matter built from nanoscopic lattices of atoms and photons (2018, background): “…correlations propagate at a distinctly different speed in the presence of long-range interactions, i.e., for power law decay 1=rα with α smaller than the system dimensionality (Hauke and Tagliacozzo, 2013; Schachenmayer et al., 2013; Gong et al., 2014; Jurcevic et al., 2014; Richerme et al., 2014).”
Many-Body Quantum Spin Dynamics with Monte Carlo Trajectories on a Discrete Phase Space (2014, background): “We study how correlations propagate throughout the system [39, 41, 42] in the presence of long-range interactions (decay exponent α = 3).”
Variational quantum algorithms for nonlinear problems (2019, background): “1(b) can capture much larger amounts of entanglement Smax[QA] ≲ d efficiently [69] and therefore this ansatz can be an efficient approximation for large values of κ1: Because the total number of variational parameters N depends linearly on d for the quantum ansatz [35], i.”
Coherent many-body spin dynamics in a long-range interacting Ising chain (2017, background): “These can entangle distant parts of the system even in the absence of moving quasiparticles [10,11,34], which arise for example in the Ising model with transverse field as free fermions after a Jordan-Wigner transformation [30].”
Non-local propagation of correlations in quantum systems with long-range interactions (2014, methodology): “As a result of (2), the third and fourth lines in equation (8) vanish.”
Quantum quenches in 1 + 1 dimensional conformal field theories (2016, background): “The standard quasi-particle picture breaks down in models with disorder, for which it has been shown that the growth of entanglement is logarithmic in time (or slower) [63, 75, 76, 77, 78, 79], and in model with long-range interactions [80, 81, 82, 83, 85].”
Quasiparticle engineering and entanglement propagation in a quantum many-body system (2014, background): “(3) Entanglement growth and simulation complexity [15] (the interaction range parameter α is known to play a critical role in the growth rate of entanglement and the possibility to simulate the dynamics with conventional computers); (4) for quasiparticle behaviour near phase transitions [30].”
Quantum thermalization through entanglement in an isolated many-body system (2016, background): “The growth of entanglement following a quench is key to understanding how entropy forms within the subsystems of a pure quantum state, thereby facilitating thermalization [2, 4, 5, 28].”