Oral: Rigorous lower bound of dynamic critical exponents in critical frustration-free systems

Quantum many-body systems are notoriously difficult to solve. One effective way to gain qualitative insights is to start with exactly solvable models and uncover the universal physics underlying them. A class of such systems called frustration-free (FF) systems have been remarkably successful in describing gapped quantum phases, providing exactly solvable examples. However, a problem arise when considering gapless phases. Notably, FF gapless systems often exhibit behavior distinct from typical gapless phases. One crucial quantity used to characterize gapless phases is the dynamic critical exponent z. While typical gapless systems exhibit z = 1, various studies have indicated that FF gapless systems tend to have z ≥ 2. This distinction is significant for two reasons. First, it highlights the limitations of FF models in capturing the nature of gapless phases. Second, it suggests that FF gapless systems represent peculiar types of gapless phases, making them intriguing subjects of study in their own right.

In our study, we establish a rigorous lower bound z ≥ 2 for FF Hamiltonians on any lattice in any spatial dimension whose ground state has a a power-law decaying correlation function. Our result also has important implications for dynamic critical phenomena. Since frustration-freeness is equivalent to reasonable conditions of locality and detailed balance in the context of Markov chains, our results provide a highly general inequality that dynamic critical exponents must satisfy.