We review the basic theory of matrix product states (MPS) as a numerical variational ansatz for time evolution, and present two methods to simulate finite temperature systems with MPS: the ancilla method and the minimally entangled typical thermal state method. A sample calculation with the Bose-Hubbard model is provided.
Cite
@article{arxiv.1008.4303,
title = {Finite Temperature Matrix Product State Algorithms and Applications},
author = {Michael L. Wall and Lincoln D. Carr},
journal= {arXiv preprint arXiv:1008.4303},
year = {2010}
}