Nonperturbative modeling of high-frequency Holstein-coupled modes using matrix product states

Many nonequilibrium phenomena of current interest involve coupling of electronic coordinates to vibrational modes whose frequency and reorganization energy are high or comparable to other relevant energies. A proper theoretical account of such modes needs to be non-perturbative and non-classical. The commonly applied direct diagonalization approach rapidly becomes prohibitively expensive with increasing system sizes. We present an alternative approach based on tensor network states, merging concepts from the condensed matter physics and molecular quantum dynamics communities. Focusing on the one-particle (electronic) sector, relevant for exciton and polaron dynamics, we construct the vibronic wavefunction as a set of matrix product states, representing the vibrational degrees of freedom surrounding the particle. This approach allows for an exact treatment of Holstein-driven processes at an unprecedented scale.