Driven one-dimensional noisy Kitaev chain

Abstract

We study one-dimensional Kitaev chain driven by the anisotropy parameter, $J_{-}=t/{\tau }_Q$, in the presence of weak Gaussian noise in the parameter $J_{+}$. The system is prepared in the ground state of the Hamiltonian at the initial time $t\to -\infty$. The defect density and the residual energy at the end of the drive protocol reveals anti-Kibble Zurek (AKZ) behavior which deviates from the earlier reported linear in quench time dependence for the defect density. The entropy density at the end of the protocol is found to exhibit the signature of the AKZ behavior. In the context of the Kitaev chain, the two-point spin correlators are short ranged. The hidden topological order across the quantum phase transition point is probed via the non-local string order parameters. The two-point Majorana correlator and the hidden string correlator calculated in the final decohered state at the end of the noisy drive protocol is consistent with the AKZ picture. We have analyzed the kink statistics in the dual spin space, the first three cumulants at the end of the noisy drive also exhibit the AKZ scaling behavior for slower sweeps similar to the defect density. The kink distribution function is well approximated with the normal distribution with non-universal noise dependent mean and variance.

References in corpus (11)

• Universal adiabatic dynamics across a quantum critical point
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Coherent quantum annealing in a programmable 2000-qubit Ising chain
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Exact results for quench dynamics and defect production in a two-dimensional model
• Entropy of entanglement and correlations induced by a quench: Dynamics of a quantum phase transition in the quantum Ising model
• Quench dynamics and defect production in the Kitaev and extended Kitaev models
• Realization of inverse Kibble-Zurek scenario with trapped Bose gases
• Non-local order parameters for the 1D Hubbard model
• Anti-Kibble-Zurek behavior of a noisy transverse-field XY chain and its quantum simulation with two-level systems

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• Entanglement generation and scaling from noisy quenches across a quantum critical point
• Separation of the Kibble-Zurek Mechanism from Quantum Criticality
• Annealing Dynamics of Regular Rotor Networks: Universality and Its Breakdown
• Topological Defects from Quantum Reset Dynamics
• Dissipation-Induced Deviations from Kibble-Zurek Scaling in Non-Hermitian Quantum Annealing