Abstract
We study the decoherence and the relaxation dynamics of topological states in an extended class of quantum Ising chains which can present a multidimensional ground state subspace. The leading interaction of the spins with the environment is assumed to be the local fluctuations of the transverse magnetic field. By deriving the Lindblad equation using the many-body states, we investigate the relation between decoherence, energy relaxation and topology. In particular, in the topological phase and at low temperature, we analyze the dephasing rates between the different degenerate ground states.
Highlights
The quantum Ising chains introduced in quantum magnetism [1,2,3,4,5,6] represent a class of exactly solvable many-body systems [7] that exemplifies one-dimensional quantum phase transitions [8,9,10,11,12]
The quantum Ising model was studied in the non-equilibrium regime to investigate the dynamical behavior of quantum phase transitions, e.g. the quenching in a driven Ising chain [13,14,15,16,17,18], the Kibble-Zurek mechanism [19, 20], the Loschmidt echo of a single impurity coupled to the Ising chain [21], the engineered quantum transfer [22], the quantum superposition of topological defects [23], the decoherence dynamics in the strong coupling regime [24] as well as the role of quantum correlations in quantum phase transitions [25,26,27]
By the analysis of the previous findings, we can restrict the dephasing dynamics in the ground state subspace, as the contribution due to the interaction with excitations scales with exp(−Egap/Θ) and can be neglected in the zero temperature limit
Summary
The quantum Ising chains introduced in quantum magnetism [1,2,3,4,5,6] represent a class of exactly solvable many-body systems [7] that exemplifies one-dimensional quantum phase transitions [8,9,10,11,12]. We generalize the results of the simple transverse Ising model by studying an extended model which includes three body, nearest neighbor interaction, with g = 2 in the topological phase In this case the ground state subspace is fourfold degenerate, with two ground states in each parity sector (even and odd) and with two zero modes whose wave functions are localized at the ends of the chain. By preparing the system in one of these excited states, we study the decay rates and the final probability of occupation of the different ground states in a (long) transient regime We show that the latter quantity is associated to the behavior of the wave functions of the Majorana zero modes and of the single particle spectrum in the topological region g = 2.
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