Efficient Simulation of Quantum Transport in 1D

Frank Pollmann (TU Munich)

Dec 01. 2021, 11:00 — 11:35

Tensor product states are powerful tools for simulating area-law entangled states of many-body systems. The applicability of such methods to the non-equilibrium dynamics of many-body systems is less clear due to the presence of large amounts of entanglement. New methods seek to reduce the numerical cost by selectively discarding those parts of the many-body wavefunction, which are thought to have relatively litte effect on dynamical quantities of interest.  We present a theory for the sizes of “backflow corrections”, i.e., systematic errors due to these truncation effects and introduce the dissipation-assisted operator evolution (DAOE) method for calculating transport properties of strongly interacting lattice systems in the high temperature regime. In the DAOE method, we represent the observable as a matrix product operator, and show that the dissipation leads to a decay of operator entanglement, allowing us to capture the dynamics to long times. We benchmark this scheme by calculating spin and energy diffusion constants in a variety of physical models and compare to other methods.

Further Information
Erwin Schrödinger Institute - virtual
Associated Event:
Topology, Disorder, and Hydrodynamics in Non-equilibrium Quantum Matter (Online Workshop)
Jörg Schmiedmayer (TU Vienna)
Maksym Serbyn (ISTA, Klosterneuburg)
Romain Vasseur (UMass Amherst)