Beecroft building

Condensed Matter Theory Forum - Effects of operator backflow on quantum transport

17 Nov 2021
Seminars and colloquia
Simpkins Lee
Martin Wood Complex, Department of Physics, University of Oxford, Parks Road, Oxford, OX1 3PU

Dr Curt von Keyserlingk (Birmingham University)

Seminar series
CMT Forum
Knowledge of physics?
Yes, knowledge of physics required
For more information contact


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 [] for details.