Quantum speed limit for a central system in Lipkin-Meshkov-Glick bath

Hou et al computed the quantum speed limit for a spin coupled to a Lipkin-Meshkov-Glick bath.

“To make this observation more precise Hou et al [173] computed the quantum speed limit for a spin coupled to a LMG bath.”

When the LMG bath is in the symmetry-broken phase, a weakly coupled probe qubit initialized in its excited state evolves at or close to the quantum speed limit, with the closeness improving for larger systems.

“By weakly coupling to the LMG environment and determining the corresponding τ QSL they showed that if the bath is in the symmetry broken phase, the probe evolves at (or close to for larger systems) the quantum speed limit.”

In the symmetric phase, where the spectral gap becomes vanishingly small with system size, the quantum speed limit time drops significantly, so the probe dynamics is significantly slower than the quantum speed limit.

“Conversely, when the bath is characterised by the symmetric phase, where the spectral gap becomes vanishingly small with system size, τ QSL witnesses a significant drop.Therefore we can conclude that the dynamics of the probe is now significantly slower than τ QSL .”

The LMG model Hamiltonian undergoes a quantum phase transition at λ = 1, and its symmetry is broken for 0 < λ < 1.

“It is further easy to see [173] that H B undergoes a quantum phase transition for λ = 1, where the symmetry is broken for 0 < λ < 1.”

The quantum speed limit of the probe system alone reflects features of the phase transition occurring in the environment.

“Hou et al [173] showed that this is indeed the case.”