Scaling of decoherence and energy flow in interacting quantum spin systems

Abstract

We address the quantum dynamics of a system composed of a qubit globally coupled to a many-body system characterized by short-range interactions. We employ a dynamic finite-size scaling framework to investigate the out-of-equilibrium dynamics arising from the sudden variation (turning on) of the interaction between the qubit and the many-body system, in particular when the latter is in proximity of a quantum first-order or continuous phase transition. Although the approach is quite general, we consider d-dimensional quantum Ising spin models in the presence of transverse and longitudinal fields, as paradigmatic quantum many-body systems. To characterize the out-of-equilibrium dynamics, we focus on a number of quantum-information oriented properties of the model. Namely, we concentrate on the decoherence features of the qubit, the energy interchanges among the qubit and the many-body system during the out-of-equilibrium dynamics, and the work distribution associated with the quench. The scaling behaviors predicted by the dynamic finite-size scaling theory are verified through extensive numerical computations for the one-dimensional Ising model, which reveal a fast convergence to the expected asymptotic behavior with increasing the system size.

arXiv comment16 pages, 9 figures

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• Noninteracting fermionic systems with localized losses: Exact results in the hydrodynamic limit
• Quantum critical systems with dissipative boundaries
• Scaling behavior of the stationary states arising from dissipation at continuous quantum transitions
• Dissipative dynamics at first-order quantum transitions
• Out-of-equilibrium dynamics arising from slow round-trip variations of Hamiltonian parameters across quantum and classical critical points
• Out-of-equilibrium finite-size scaling in generalized Kibble-Zurek protocols crossing quantum phase transitions in the presence of symmetry-breaking perturbations
• Decoherence and energy flow in the sunburst quantum Ising model
• Quantum critical behaviors and decoherence of weakly coupled quantum Ising models within an isolated global system
• Stacked quantum Ising systems and quantum Ashkin-Teller model
• Quantum many-body spin rings coupled to ancillary spins: The sunburst quantum Ising model