The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied for the first time to a model suffering the notorious quantum Monte Carlo sign problem --- the orbital eg model with spatially highly anisotropic orbital interactions. Coarse-graining of the tensor network along the inverse temperature β yields a numerically tractable 2D tensor network representing the Gibbs state. Its bond dimension D --- limiting the amount of entanglement --- is a natural refinement parameter. Increasing D we obtain a converged order parameter and its linear susceptibility close to the critical point. They confirm the existence of finite order parameter below the critical temperature Tc, provide a numerically exact estimate of~Tc, and give the critical exponents within 1% of the 2D Ising universality class.
@article{arxiv.1703.03586,
title = {Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital $e_g$ Model on an Infinite Square Lattice},
author = {Piotr Czarnik and Jacek Dziarmaga and Andrzej M. Oleś},
journal= {arXiv preprint arXiv:1703.03586},
year = {2017}
}