# Approximating the long time average of the density operator: Diagonal ensemble

Aslı Çakan, J. Ignacio Cirac, and Mari Carmen Bañuls
Phys. Rev. B 103, 115113   Published 2021

## 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 [M. C. Bañuls, D. A. Huse, and J. I. Cirac, Phys. Rev. B 101, 144305 (2020)] to this problem. We analyze the performance of the method on a nonintegrable spin chain, for which we observe that local observables converge towards thermal values polynomially with the inverse width of the filter.