Breaking the entanglement barrier: Tensor network simulation of quantum transport

Abstract

The recognition that large classes of quantum many-body systems have limited entanglement in the ground and low-lying excited states led to dramatic advances in their numerical simulation via so-called tensor networks. However, global dynamics elevates many particles into excited states, and can lead to macroscopic entanglement and the failure of tensor networks. Here, we show that for quantum transport -- one of the most important cases of this failure -- the fundamental issue is the canonical basis in which the scenario is cast: When particles flow through an interface, they scatter, generating a "bit" of entanglement between spatial regions with each event. The frequency basis naturally captures that -- in the long-time limit and in the absence of inelastic scattering -- particles tend to flow from a state with one frequency to a state of identical frequency. Recognizing this natural structure yields a striking -- potentially exponential in some cases -- increase in simulation efficiency, greatly extending the attainable spatial- and time-scales, and broadening the scope of tensor network simulation to hitherto inaccessible classes of non-equilibrium many-body problems.

Published version; 6+9 pages; 4+4 figures; Added: an example of interacting reservoirs, further evidence on performance scaling, and extended discussion of the numerical details

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