**GLAM Special Seminar
Geballe Laboratory for Advanced Materials**

Monday, 29 Nov 2021 at 3:00 p.m.

Location: IN-PERSON McCullough 335 and Zoom

Note: seating is limited

Host: Tibor Rakovszky

**Curt von Keyserlingk**

University of Birmingham

**Operator backflow and the classical simulation of quantum transport**

Tensor product states have proved extremely powerful for simulating the area-law entangled states of many-body systems, such as the ground states of gapped Hamiltonians in one dimension. The applicability of such methods to the \emph{dynamics} of many-body systems is less clear: the memory required grows exponentially in time in most cases, quickly becoming unmanageable. New methods reduce the memory required by selectively discarding/dissipating parts of the many-body wavefunction which are expected to have little effect on the hydrodynamic observables typically of interest: for example, some methods discard fine-grained correlations associated with $n$-point functions, with $n$ exceeding some cutoff $\ell_*$. In this work, we present a theory for the sizes of `backflow corrections', i.e., systematic errors due to discarding this fine-grained information. In particular, we focus on their effect on transport coefficients. Our results suggest that backflow corrections are exponentially suppressed in the size of the cutoff $\ell_*$. Moreover, the backflow errors themselves have a hydrodynamical expansion, which we elucidate. We test our predictions against numerical simulations run on random unitary circuits and ergodic spin-chains. These results lead to the conjecture that transport coefficients in ergodic diffusive systems can be captured to a given precision $\epsilon$ with an amount of memory scaling as $\exp[\mathcal{O}(\log(\epsilon)^2)]$, significantly better than the naive estimate of memory $\exp[\mathcal{O}(\mathrm{poly}(\epsilon^{-1}))]$ required by more brute-force methods.