  In this work we propose a series-expansion thermal tensor network (SETTN)
approach for efficient simulations of quantum lattice models. This
continuous-time SETTN method is based on the numerically exact Taylor series
expansion of equilibrium density operator $e^{-\beta H}$ (with $H$ the total
Hamiltonian and $\beta$ the imaginary time), and is thus Trotter-error free. We
discover, through simulating XXZ spin chain and square-lattice quantum Ising
models, that not only the Hamiltonian $H$, but also its powers $H^n$, can be
efficiently expressed as matrix product operators, which enables us to
calculate with high precision the equilibrium and dynamical properties of
quantum lattice models at finite temperatures. Our SETTN method provides an
alternative to conventional Trotter-Suzuki renormalization group (RG)
approaches, and achieves an unprecedented standard of thermal RG simulations in
terms of accuracy and flexibility.
