Description
TNS provide efficient approximations of thermal equilibrium states. The most common algorithm constructs a purification of the thermal state starting from infinite temperature and evolving the state in imaginary time towards lower temperature. At very low temperatures, this has the practical drawback of trying to approximate a low rank density operator via a full rank one. We present a complementary ansatz, constructed from the zero-temperature limit, the ground state, which can be found with a standard tensor network approach. Motivated by properties of the ground state for conformal field theories, our ansatz is especially well-suited near criticality. Moreover, it allows an efficient computation of thermodynamic quantities and entanglement properties. We demonstrate the performance of our approach with a tree tensor network ansatz, although it can be extended to other tensor networks, and present results illustrating its effectiveness in capturing the finite-temperature properties in one- and two-dimensional scenarios. In particular, in the critical 1D case we show how the ansatz reproduces the finite temperature scaling of entanglement in a CFT.
