Finding the Dynamics of an Integrable Quantum Many-Body System via Machine Learning

The dynamics of the Gaudin magnet ("central-spin model") is studied using machine-learning methods. This model is of practical importance, for example, for studying non-Markovian decoherence dynamics of a central spin interacting with a large bath of environmental spins and for studies of nonequilibrium superconductivity. The Gaudin magnet is also integrable, admitting many conserved quantities. Machine-learning methods may be well suited to exploiting the high degree of symmetry in integrable problems, even when an explicit analytic solution is not obvious. Motivated in part by this intuition, a neural-network representation (restricted Boltzmann machine) is used for each variational eigenstate of the model Hamiltonian. Accurate representations of the ground state and of the low-lying excited states of the Gaudin-magnet Hamiltonian are then obtained through a variational Monte Carlo calculation. From the low-lying eigenstates, the non-perturbative dynamic transverse spin susceptibility is found, describing the linear response of a central spin to a time-varying transverse magnetic field in the presence of a spin bath. Having an efficient description of this susceptibility opens the door to improved characterization and quantum control procedures for qubits interacting with an environment of quantum two-level systems. Machine-learning methods are used to find nonperturbative dynamics of the Gaudin magnet (central-spin model). The Gaudin magnet has important applications in qubit dynamics/decoherence and in nonequilibrium superconductivity. Integrable models like the Gaudin magnet have many conserved quantities and their dynamics may therefore admit an efficient machine-learning solution even when an analytic solution is not evident. image