Overcoming the sign problem at finite temperature: Quantum tensor network for the orbital eg model on an infinite square lattice

The variational tensor network renormalization approach to two-dimensional (2D) quantum systems at finite temperature is applied to a model suffering the notorious quantum Monte Carlo sign problem-the orbital e(g) model with spatially highly anisotropic orbital interactions. Coarse graining of the tensor network along the inverse temperature beta 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 T-c, provide a numerically exact estimate of T-c, and give the critical exponents within 1% of the 2D Ising universality class.