Thermal Pure States for Systems with Antiunitary Symmetries

The eigenstate thermalization hypothesis (ETH) plays a key role in explaining the thermalization of isolated quantum many-body systems. It implies that all energy eigenstates are thermal pure states, locally indistinguishable from equilibrium states. Despite its significance, the verification relies on numerical simulations, as the theoretical treatment of energy eigenstates is extremely difficult. Several methods for constructing thermal pure states have been proposed, providing valuable insights into the ETH. However, these states are based on Haar random states, so there is a gap between them and actual energy eigenstates. We propose a novel method to construct thermal pure states for systems with certain antiunitary symmetries. These states are generated from theoretically tractable states, called entangled antipodal pair states, originally introduced as exact thermal eigenstates of nonintegrable systems at infinite temperature. Our results suggest the high expressivity of states derived from entangled antipodal pair states, offering a new approach for analyzing volume-law states, including finite-temperature energy eigenstates. Moreover, despite obeying the volume law, these thermal pure states can be efficiently represented with tensor networks due to their simple structure.