Special PME Quantum Seminar - Sajant Anand

Efficient classical simulation of infinite-temperature operator dynamics beyond one-dimensional, local spin chains

The use of tensor networks (TNS) for simulating time dynamics is limited by the linear growth of entanglement entropy in time for generic, interacting quantum systems. Recently, however, various TNS algorithms have been developed to study operator dynamics at infinite temperature in one-dimensional local models, where significant simplifications can be made. Here, we extend the Density Matrix Truncation algorithm to simulate the dynamics of mixed states and operators with long-range Hamiltonians with matrix product states (MPS), demonstrating that a more nuanced interpretation of the Schmidt operator Hilbert space is crucial for accurate simulations. With these methods, we study charge transport at infinite temperature in both two- (2D) and three-dimensional (3D) models, both generic and integrable. In particular, we determine the energy diffusion constant for the 2D and 3D mixed-field transverse field Ising models and study the ballistic-to-diffusive and superdiffusive-to-diffusive crossover for energy and spin transport in the two-dimensional Heisenberg model on ladders, respectively. Finally, we comment on extensions beyond MPS algorithms and infinite temperature transport.