Optimal sampling of dynamical large deviations via matrix product states

The large deviation statistics of dynamical observables is encoded in the spectral properties of deformed Markov generators. Recent works have shown that tensor network methods are well suited to compute accurately the relevant leading eigenvalues and eigenvectors. However, the efficient generation of the corresponding rare trajectories is a harder task. Here, we show how to exploit the matrix product state approximation of the dominant eigenvector to implement an efficient sampling scheme which closely resembles the optimal (so-called Doob) dynamics that realizes the rare events. We demonstrate our approach on three well-studied lattice models, the Fredrickson-Andersen and East kinetically constrained models, and the symmetric simple exclusion process. We discuss how to generalize our approach to higher dimensions.

Automated summary

The paper discusses how tensor network methods can accurately compute the spectral properties of deformed Markov generators, and demonstrates an efficient sampling scheme using matrix product state approximation of dominant eigenvectors. The approach is applied to three lattice models and potential generalizations to higher dimensions are discussed.