Theory Seminar: A new tool to approximate the diagonal ensemble

Asli Cakan (MPQ):
For an isolated generic Hamiltonian with nondegenerate spectrum, the long time limit of time-averaged observables corresponds to the expectation value in the diagonal ensemble.

Asli Cakan (MPQ)
Group seminar via Zoom
Mon, 13 December 2021, 11:30 am (MEZ)

Abstract:

For an isolated generic Hamiltonian with nondegenerate spectrum, the long time limit of time-averaged observables corresponds to the expectation value in the diagonal ensemble. To decide whether the system can thermalize, it is enough to compare the expectation values in the diagonal ensemble to those in thermal equilibrium at the same energy. But while the thermal state of a local Hamiltonian can be efficiently approximated using tensor networks, simulating the out-of-equilibrium dynamics, and thus directly constructing the diagonal ensemble, is a much harder problem. We know that some numerical methods have been developed that can approximate the diagonal ensemble, however, restricted to the small systems or short times. In this talk I will introduce an alternative method to find a tensor network approximation to the diagonal ensemble, which allows us to treat larger systems than exact diagonalization and analyze the convergence of local observables towards the thermal equilibrium.

If you'd like to participate in the seminar, please contact us!