Entanglement dynamics of an Ising spin chain coupled to a central ancilla

Characterizing the spread of entanglement in many-body quantum systems is of both fundamental and applied interest. Coupling a controllable ancilla to a many-body system could allow us to quantify the entanglement dynamics of a system. Two important questions that arise are: 1) what information can we gain about the system by measuring the ancilla? and 2) does the ancilla influence the entanglement dynamics of the system? Szabo and Trivedi have characterized the entanglement dynamics of the transverse field Ising chain with the spins coupled uniformly to a central bosonic ancilla using different entanglement metrics including a novel one called multipartite entanglement loss (MEL) [1]. In this work, we augment this investigation using the eigenstate entanglement spectrum (EES) and the entanglement spectrum statistics (ESS) and compare the insights to those from the MEL. EES characterizes the bipartite entanglement of eigenstates of the many-body Hamiltonian. ESS characterizes the growth of bipartite entanglement during time evolution of an initial product state under the Hamiltonian. We use exact diagonalization to explore the transition of the statistics from a Gaussian Orthogonal Ensemble (GOE) to a Poisson distribution as the transverse field strength and the coupling strength to the ancilla are varied. Finally, we replace the central bosonic ancilla with a spin qubit and explore the consequences of non-uniform spin-ancilla couplings.



[1] J. C. Szabo and N. Trivedi, Phys. Rev. A 105, 052431 (2022)