We propose the construction of thermodynamic ensembles that minimize the Rényi free energy, as an alternative to Gibbs states. For large systems, the local properties of these Rényi ensembles coincide with those of thermal equilibrium and they can be used as approximations to thermal states. We provide algorithms to find tensor network approximations to the 2-Rényi ensemble. In particular, a matrix-product-state representation can be found by using gradient-based optimization on Riemannian manifolds or via a nonlinear evolution which yields the desired state as a fixed point. We analyze the performance of the algorithms and the properties of the ensembles on one-dimensional spin chains.

• Received 14 January 2021
• Revised 21 April 2021
• Accepted 21 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.205128

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

Published by the American Physical Society