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arXiv · 1703.03586

Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital $e_g$ Model on an Infinite Square Lattice

Piotr Czarnik·Jacek Dziarmaga·Andrzej M. Oleś
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Abstract

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 $e_g$ 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.

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Piotr Czarnik, Jacek Dziarmaga, Andrzej M. Oleś. 2017-03-10. Overcoming the Sign Problem at Finite Temperature: Quantum Tensor Network for the Orbital $e_g$ Model on an Infinite Square Lattice. https://doi.org/10.1103/physrevb.96.014420

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