Small Matrix Path Integral with Extended Memory

The small matrix decomposition of the path integral (SMatPI) for a discrete system coupled to a harmonic bath expresses the reduced density matrix in terms of matrices whose size is given by the number of states comprising the system, circumventing the large storage requirements of iterative tensor-based algorithms. The present work extends the SMatPI methodology to account for residual memory that exceeds the entanglement length without an increase in computational effort.