Effects of operator backflow on quantum transport

Tensor product states have proved extremely powerful for simulating the low-temperature properties of many-body systems. The applicability of such methods to the dynamics of many-body systems is less clear: as entanglement grows under time evolution, memory requirements or truncation errors spiral out of control. In this talk, we present a method that seeks to reduce this memory barrier by selectively discarding highly non-local correlations in a controlled manner. We illustrate our method on various model systems and develop a theory to estimate the size of the error from the neglected "backflow" processes from nonlocal to local quantities. Our results suggest that backflow errors are exponentially suppressed in the size-cutoff; based on this result, we conjecture that the numerical resources needed to capture transport coefficients in ergodic diffusive systems scale effectively polynomially with the required precision, significantly better than the exponential scaling of more brute-force methods. We also discuss how our method performs compared to other approximation schemes.