We develop the parquet-diagram summation method for neutron matter interacting via potentials that include spin, tensor, and spin-orbit components. For that purpose, we derive an exact expression for the sum of all ring diagrams in terms of effective local particle-hole interactions involving the above four operators. The parquet equations are closed by deriving the spin-orbit contribution to those particle-hole interactions. We show that many-body correlations screen the bare spin-orbit potential considerably, and the corrections of that screened spin-orbit potential to the other three interaction channels are quite small. We apply our method to the calculation of the response of neutron matter to density and both longitudinal and transverse spin-dependent external fields.
Tensor networks are adopted to calculate the responses for one-dimensional quantum spin systems that are initially in thermal equilibrium. The Ising chain in mixed transverse and longitudinal fields is used as the benchmarking system. The linear and second-order responses of the magnetization in
z-direction induced by the time-dependent force conjugated with the magnetization in
x-direction are calculated. In addition, the magnetization in
z-direction is also exactly calculated in response to this excitation. As expected, the first two responses are shown to be excellent corrections to the equilibrium magnetization in
z-direction when the excitation is weak. This result represents an illustrative example of the response theory for nontrivial quantum many-body systems.