Thermal pure states for systems with antiunitary symmetries and their tensor network representations

Thermal pure state algorithms, which employ pure quantum states representing thermal equilibrium states instead of statistical ensembles, are useful both for numerical simulations and for theoretical analysis of thermal states. However, their inherently large entanglement makes it difficult to represent efficiently and limits their use in analyzing large systems. Here we propose a tensor network algorithm for constructing thermal pure states for systems with certain antiunitary symmetries, such as time-reversal or complex-conjugate symmetry. Our method utilizes thermal pure states that, while exhibiting volume-law entanglement, can be mapped to tensor network states through simple transformations. Furthermore, our approach does not rely on random sampling and thus avoids statistical uncertainty. Moreover, we can compute not only thermal expectation values of local observables but also thermodynamic quantities. We demonstrate the validity and utility of our method by applying it to the one-dimensional XY model and the two-dimensional Ising model on a triangular lattice. Our results suggest a class of variational wave functions for volume-law states that are not limited to thermal equilibrium states.