Martin Wood Complex, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU
Dr Curt von Keyserlingk (Birmingham University)
Max McGinley maximilian.mcginley@physics.ox.ac.uk
Abstract
Tensor product states have proved extremely powerful for simulating the area-law entangled states of many-body systems, such as gapped ground states in one dimension. The applicability of such methods to the dynamics of many-body systems is less clear: the memory required grows exponentially in time in most cases, quickly becoming unmanageable. New methods seek to reduce the memory required by selectively discarding/dissipating those parts of the many-body wavefunction which are thought to have little effect on observables of interest. The sorts of information discarded are, in some cases, fine-grained correlations associated with e.g., $n$-point function 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 these truncation effects. We test our predictions against numerical simulations run on a random circuit and ergodic spin-chains. Our results suggest that backflow errors are exponentially suppressed in the size of the cutoff $\ell_*$; with this result, we 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. Moreover, the backflow errors themselves have a hydrodynamical expansion, which we elucidate.
If you would like to attend this meeting online, a Zoom link will be available. Please contact Max McGinley [maximilian.mcginley@physics.ox.ac.uk] for details.