Tradeoffs Between Thermal and Quantum Fluctuations in 2D Systems

Under a certain set of conditions collectively known as "local topological order", the low energy spectrum of a system is robust to local perturbations. This has the consequence that quantum information encoded in the degenerate ground state of such a system is stable at zero temperature. On the other hand, the existence of a macroscopic energy barrier between ground states imply that information encoded in the ground state is robust against thermal fluctuations. Here, we demonstrate that for local commuting projector codes, local topological order prohibits the existence of an energy barrier, which shows a tradeoff between robustness to quantum and thermal fluctuations. I will also discuss relations to area law and quantum Markov networks.