Abstract
For an isolated generic quantum system out of equilibrium, the long time average of observables is given by the diagonal ensemble, i.e. the mixed state with the same probability for energy eigenstates as the initial state but without coherences between different energies. In this work we present a method to approximate the diagonal ensemble using tensor networks. Instead of simulating the real time evolution, we adapt a filtering scheme introduced earlier in [Phys. Rev. B 101, 144305 (2020)] to this problem. We analyze the performance of the method on a non-integrable spin chain, for which we observe that local observables converge towards thermal values polynomially with the inverse width of the filter.
Highlights
When an isolated quantum system is initialized in a pure state out of equilibrium, the unitary character of the evolution ensures that the state remains pure at any later times
For a generic Hamiltonian with nondegenerate spectrum, the long time limit of time-averaged observables corresponds to the expectation value in the diagonal ensemble [8]
We have presented a method to approximate the diagonal ensemble corresponding to a quantum many-body state
Summary
When an isolated quantum system is initialized in a pure state out of equilibrium, the unitary character of the evolution ensures that the state remains pure at any later times. For a generic Hamiltonian with nondegenerate spectrum, the long time limit of time-averaged observables corresponds to the expectation value in the diagonal ensemble [8] This mixed state, diagonal in the energy eigenbasis, can be seen as the average of the density operator of the system at all times. While the thermal state of a local Hamiltonian can be efficiently approximated using tensor networks [9,10,11], simulating the out-of-equilibrium dynamics, and directly constructing the diagonal ensemble, is a much harder problem [12,13]. VI we summarize our findings and discuss potential extensions of our work
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
