Open system probes of many-body environments: Zero temperature limit

Markovian dynamics typically coincide with large thermal environments; however, they have also been observed in "stiff" environments at critical points. In this work, we further probe the connection between Markovianity and criticality by revisiting the dephasing dynamics of a qubit coupled to a transverse field Ising model (TFIM), represented as a theory of massive Majorana fermions. In part one of this two-part talk, we construct the (non-Markovian) Redfield quantum master equation (QME) for the probe qubit by explicitly tracing over the Majorana environment. We consider the environment in its ground state and employ the QME [1] to analytically calculate dephasing rates of the qubit both at and away from criticality. We benchmark these rates against exact results obtained using the Loschmidt echo and, remarkably, find quantitative agreement between the two even at criticality. For any non-zero fermion mass, we find an asymptotically vanishing decay rate leading to a decoupling of the system and environment. Using the recently proposed spectral measure of non-Markovianity [2], we show how the probe spectrum can be used to directly observe the many-body spectral gap.

[1] B. Bowen, N. Agarwal, A. Kamal. arXiv:2403.18907 (2024)

[2] A. Keefe, N. Agarwal, A. Kamal. arXiv:2405.01722 (2024)