Quantum Dynamics of Matrix Product States on Transformed bases

Numerical simulation of the quantum states under the unitary evolution with generic non-integrable Hamiltonians still remains a challenge. The exact diagonaliztion (ED) method only works for very small system sizes and methods based on matrix product states (MPS), such as time dependent variational principle (TDVP) fail to capture long time behavior of the systems, such as the diffusion constant, with controlled precision. The main culprit is believed to be the rapid entanglement growth to volume-law in real space cuts. The entanglement blow-up makes the long-times inaccessible for variational ansatz that are designed to represent states with area-law entanglement entropy. In this work, we explore a MPS time evolution but on a set of transformed bases that are local both in real and fourier space. We benchmark this method on the anti-ferromagnetic Heisenberg chain with longer range exchange terms to bring the system our of integrability. We demonstrate the possibility of achieving longer time simulations by comparing the results to exact ED as well as TDVP on real space.