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Finite temperature problems in the strong correlated systems are importantbut challenging tasks. Minimally entangled typical thermal states (METTS) are apowerful method in the framework of tensor network methods to simulate finitetemperature systems, including Fermions and frustrated spins which introduce asign problem in the typical Monte Carlo methods. In this work, we introduce anextension of the METTS algorithm by using a new basis, the auxiliary matrixproduct state. This new basis achieves the pre-summation process in thepartition function, and thus improve the convergence in the Monte Carlosamplings. The method also has the advantage of simulating the grand canonicalensemble in a computationally efficient way by employing good quantum numbers.We benchmark our method on the spin-$1/2$ XXZ model on the triangular lattice,and show that the new method outperforms the original METTS as well as thepurification methods at sufficiently low temperature, the usual range ofapplications of METTS. The new method also naturally connects the METTS methodto the purification method.

Minimally entangled typical thermal states with auxiliary matrix-product-state bases