Efficient simulation of low-temperature physics in one-dimensional gapless systems

We discuss the computational efficiency of the finite-temperature simulation with minimally entangled typical thermal states (METTS). To argue that METTS can be efficiently represented as matrix product states, we present an analytic upper bound for the average entanglement Rényi entropy of METTS for a Rényi index $0<q\le 1$. In particular, for one-dimensional (1D) gapless systems described by conformal field theories, the upper bound scales as $O(c{N}^{0}log\beta )$ where $c$ is the central charge and $N$ is the system size. Furthermore, we numerically find that the average Rényi entropy exhibits a universal behavior characterized by the central charge and is roughly given by half of the analytic upper bound. Based on these results, we show that METTS can provide a speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.