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The European Physical Journal Plus

Quantum phase transition with non-Markovianity of XY model under three-spin interaction and quantum speed limit time of a centrally interacting spin qubit

Muhammad Musadiq, Salman Khan

Published Oct 1, 2021• 6 citations
Publisher
DOI
10.1140/epjp/s13360-021-01974-z

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We explore quantum speed limit time τQSL of a qubit system coupling to a spin chain environment which is described by an extended Ising model associated with non-trivial topological characterization. For an initial pure state, we find that τQSL exhibits a behavior of local maximum around all critical points when the environment spin chain undergoes a topological quantum phase transition driven by external magnetic field λ or the anisotropy γ of nearest-neighbor interaction. And the value of local maximum would increase by strengthening the coupling between the system and environment around the critical points. However, the behavior of τQSL are both driving parameters and critical points dependent when the topological quantum phase transition is driven by the three-site interaction α or its anisotropy δ. Additionally, we also investigate τQSL for arbitrary time-evolution state in the whole dynamics process and find that τQSL exhibits a behavior of oscillation at non-critical points. However, τQSL will decay rapidly to zero around all critical points, and such trend accompany with oscillation behavior at some critical points.

•Jan 1, 2022•0 citations
Abstract We study the dynamics of quantum speed limit (QSL) time of a central spin, uniformly interacting with the spins of an Ising spin chain placed in a transverse magnetic field, and the non-Markovianity of the spin environment. Both pure and time dependent mixed initial states of the central spin are taken into account. For a pure initial state, both the quantities work as indicators for quantum phase transition (QPT) and can locate the critical point (CP). For a time dependent mixed initial state of the central spin, QSL time also shows anomalous behavior in the vicinity of the CP, a signature of signaling QPT. The numerical simulations show that the spin environment has potential capacity for speeding up quantum evolution, which can be manipulated through the strength of the applied magnetic field.
We explore quantum speed limit time τQSL of a qubit system coupling to a spin chain environment which is described by an extended Ising model associated with non-trivial topological characterization. For an initial pure state, we find that τQSL exhibits a behavior of local maximum around all critical points when the environment spin chain undergoes a topological quantum phase transition driven by external magnetic field λ or the anisotropy γ of nearest-neighbor interaction. And the value of local maximum would increase by strengthening the coupling between the system and environment around the critical points. However, the behavior of τQSL are both driving parameters and critical points dependent when the topological quantum phase transition is driven by the three-site interaction α or its anisotropy δ. Additionally, we also investigate τQSL for arbitrary time-evolution state in the whole dynamics process and find that τQSL exhibits a behavior of oscillation at non-critical points. However, τQSL will decay rapidly to zero around all critical points, and such trend accompany with oscillation behavior at some critical points.