A general spectral method for the numerical simulation of one-dimensional interacting fermions

is work introduces a general framework for the direct numerical simulation of systems of interacting fermions in one spatial dimension. e approach is based on a specially adapted nodal spectral Galerkin method, where the basis functions are constructed to obey the antisymmetry relations of fermionic wave functions. An e›cient Matlab program for the assembly of the stišness and potential matrices is presented, which exploits the combinatorial structure of the sparsity pattern arising from this discretization to achieve optimal run-time complexity. is program allows the accurate discretization of systems with multiple fermions subject to arbitrary potentials, e. g., for verifying the accuracy of multi-particle approximations such as Hartree–Fock in the few-particle limit. It can be used for eigenvalue computations or numerical solutions of the timedependent Schrödinger equation.