Quenching across quantum critical points: role of topological patterns

Abstract

We introduce a one-dimensional version of the Kitaev model consisting of spins on a two-legged ladder and characterized by Z_2 invariants on the plaquettes of the ladder. We map the model to a fermionic system and identify the topological sectors associated with different Z_2 patterns in terms of fermion occupation numbers. Within these different sectors, we investigate the effect of a linear quench across a quantum critical point. We study the dominant behavior of the system by employing a Landau-Zener-type analysis of the effective Hamiltonian in the low-energy subspace for which the effective quenching can sometimes be non-linear. We show that the quenching leads to a residual energy which scales as a power of the quenching rate, and that the power depends on the topological sectors and their symmetry properties in a non-trivial way. This behavior is consistent with the general theory of quantum quenching, but with the correlation length exponent νbeing different in different sectors.

5 pages including 2 figures; this is the published version

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• Topological Blocking in Quantum Quench Dynamics
• Non-equilibrium quantum relaxation across a localization-delocalization transition
• Dynamical critical scaling and effective thermalization in quantum quenches: the role of the initial state
• Fingerprints of Majorana bound states in Aharonov Bohm geometry
• Edge mode dynamics of quenched topological wires
• Spin-1 Kitaev model in one dimension
• Fidelity susceptibility of one-dimensional models with twisted boundary conditions
• Nonequilibrium dynamics of the Ising chain in a fluctuating transverse field
• Driven one-dimensional noisy Kitaev chain
• Quenching across quantum critical points in periodic systems: dependence of scaling laws on periodicity
• Transport across a system with three p-wave superconducting wires: effects of Majorana modes and interactions
• Quantum charge pumping through Majorana bound states