Matrix product state algorithms for Gaussian fermionic states

Simulation methods for real materials often require the solution of extremely large inhomogeneous systems of noninteracting fermions. Here, the authors show how the density matrix renormalization group (DMRG), the most successful method for 1D interacting systems, can be adapted to noninteracting fermions, giving a significant improvement both over conventional DMRG and over the full solution of the noninteracting problem. The authors test the method on a range of one- and two-dimensional examples for both static and dynamic properties, demonstrating its applicability to systems up to a million sites.