Unifying time evolution and optimization with matrix product states

We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimization methods in the context of matrix product states. In particular, we introduce a new integration scheme for studying time evolution, which can cope with arbitrary Hamiltonians, including those with long-range interactions. Rather than a Suzuki-Trotter splitting of the Hamiltonian, which is the idea behind the adaptive time-dependent density matrix renormalization group method or time-evolving block decimation, our method is based on splitting the projector onto the matrix product state tangent space as it appears in the Dirac-Frenkel time-dependent variational principle. We discuss how…

• DF
  Deutsche Forschungsgemeinschaft

  Awards: SPP 1324, GRK 1838
• AS
  Austrian Science Fund
• RS
  Russian Science Foundation

  Award: 14-11-00659