Efficient Simulation of Low Temperature Physics in One-Dimensional Gapless Systems

We discuss the computational efficiency of the finite temperature simulation with the 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 Renyi entropy of METTS for Renyi index $0<q\leq 1$. In particular, for 1D gapless systems described by CFTs, the upper bound scales as $\mathcal{O}(c N^0 \log \beta)$ where $c$ is the central charge and $N$ is the system size. Furthermore, we numerically find that the average Renyi 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 provide a significant speedup compared to employing the purification method to analyze thermal equilibrium states at low temperatures in 1D gapless systems.