Towards finite-temperature tensor network simulations of the two-dimensional Hubbard model

The phase diagram of the two-dimensional Hubbard model at finite temperature poses one of the most interesting conundrums in contemporary condensed matter physics. Tensor network techniques, such as matrix-product based approaches as well as 2D tensor networks (PEPS), yield state-of-the-art unbiased simulations of the 2D Hubbard model at zero temperature and are capable of giving unbiased results at finite temperature as well. A promising approach for applying tensor networks to study finite-temperature quantum systems is the minimally entangled typical thermal state (METTS) algorithm, which is a Monte Carlo technique that samples from a family of entangled wavefunctions, and which offers favorable scaling and parallelism. We demonstrate how the METTS algorithm in combination with modern time-evolution algorithms for matrix-product states, like the time-dependent variational principle (TDVP) method, allows simulating the Hubbard model at finite temperature for cylinder geometries approaching the two-dimensional limit.