Reduced basis emulation of pairing in finite systems

In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they used, largely in nuclear physics, as fast emulators able bypass expensive direct computations while still providing highly accurate results. This work is meant show that RBM an efficient emulator for strong correlations induced by pairing interaction a variety of finite systems like ultrasmall superconducting grains, interacting topological superfluids mesoscopic hybrid superconductor-semiconductor devices, all which require expensive, beyond-mean-field, particle-number conserving description. These are modelled number-conserving Richardson Hamiltonian its appropriate generalizations. Their ground state solved exactly using Density Matrix Renormalization Group. The assembled iteratively from small number exact vectors, well-chosen across relevant parameter space estimate emulation error greedy local optimization algorithm. found accurately describe weak-to-strong cross-over third-order phase transition Richardson-Kitaev chain, complex charge stability diagram quantum dot - superconductor device. RBMs thus confirmed be cheap widely encountered phenomena. Capable orders magnitude computational speed-up with respect approaches based only on traditional solvers, open new possibilities building solving models better interfacing them experimental design data analysis.