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The Minimally Entangled Typical Thermal States (METTS) are an ensemble ofpure states, equivalent to the Gibbs thermal state, that can be efficientlyrepresented by tensor networks. In this article, we use the Projected EntangledPair States (PEPS) ansatz as to represent METTS on a two-dimensional (2D)lattice. While Matrix Product States (MPS) are less efficient for 2D systemsdue to their complexity growing exponentially with the lattice size, PEPSprovide a more tractable approach. To substantiate the prowess of PEPS inmodeling METTS (dubbed as PEPS-METTS), we benchmark it against the purificationmethod for the 2D quantum Ising model at its critical temperature. Our analysisreveals that PEPS-METTS achieves accurate long-range correlations withsignificantly lower bond dimensions. We further corroborate this finding in the2D Fermi Hubbard model at half-filling. At a technical level, we introduce anefficient \textit{zipper} method to obtain PEPS boundary matrix product statesneeded to compute expectation values. The imaginary time evolution is performedwith the neighbourhood tensor update.

Efficient Representation of Minimally Entangled Typical Thermal States in two dimensions via Projected Entangled Pair States