Finite-temperature quantum many-body systems and thermal tensor networks

Thermal states of quantum lattice models, which are of great interest both theoretically and experimentally, satisfy an area law of mutual information. Thermal tensor networks could provide an efficient representation for thermal states in the quantum many-body systems with local interactions. Renormalization group (RG) methods based on the world-line Trotter-Suzuki decomposition, including the transfer-matrix RG and finite-temperature density-matrix RG,constitute an important class of thermal tensor network methods. On the other hand, inspired by the stochastic series expansion (SSE) quantum Monte Carlo method, recently we developed a series-expansion thermal tensor network (SETTN) method realizing an RG thermal calculation in essentially continuous time and therefore with no discretization error. Furthermore, unlike the SSE method, SETTN does not suffer from the notorious negative sign problem. Besides onedimensional cases, we also discuss two possible routes, i.e., the matrix-product and the tensorproduct operators, to generalize the thermal tensor network algorithms to two dimensions.