Low-Temperature Gibbs States with Tensor Networks

Abstract: We introduce a tensor network method for approximating thermal equilibrium states of quantum many-body systems at low temperatures. In contrast to standard (thermofield double matrix product state) algorithms, our ansatz is constructed from the zero-temperature limit, the ground state, which can be simply found with a standard tensor network approach. This method allows us to efficiently compute thermodynamic quantities and entanglement properties. We demonstrate our approach within 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 the $1\mathrm{D}$ and $2\mathrm{D}$ scenario.