Exact dynamical correlations of nonlocal operators in quadratic open Fermion systems: a characteristic function approach

Abstract

The dynamical correlations of nonlocal operators in general quadratic open fermion systems is still a challenging problem. Here we tackle this problem by developing a new formulation of open fermion many-body systems, namely, the characteristic function approach. Illustrating the technique, we analyze a finite Kitaev chain with boundary dissipation and consider anyon-type nonlocal excitations. We give explicit formula for the Green's functions, demonstrating an asymmetric light cone induced by the anyon statistical parameter and an increasing relaxation rate with this parameter. We also analyze some other types of nonlocal operator correlations such as the full counting statistics of the charge number and the Loschmidt echo in a quench from the vacuum state. The former shows clear signature of a nonequilibrium quantum phase transition, while the later exhibits cusps at some critical times and hence demonstrates dynamical quantum phase transitions.

Nonlocal correlations in noisy multiqubit systems simulated using matrix product operators

“…We note that the parameters g 0,i describe transfer of population to the eigenstate of σ z i with eigenvalue +1, which is in the product ground state of the Hamiltonian in Eq. (20) in the absence of driving. In qubit devices the environment temperature is typically significantly lower than the qubit's energy gap, and hence keeping the spontaneous emission terms only and neglecting the energy excitation process is typically an accurate approximation [60].…”

“…Qubit 0 on the left edge is being driven periodically as in Eq. (20), and the qubits interact with with their nearest neighbors by a "flip-flop" (XY) interaction term as in Eq. ( 21).…”