| Speaker: | Rintaro Masaoka (Dept. of Applied Physics, U. Tokyo) |
|---|---|
| Title: | Rigorous lower bound of dynamic critical exponents in critical frustration-free systems |
| Date (JST): | Tue, Oct 29, 2024, 13:30 - 15:00 |
| Place: | Balcony B |
| Abstract: |
Frustration-free systems are quantum systems that are theoretically tractable, characterized by ground states that minimize all local terms in the Hamiltonian simultaneously. Despite their specific nature, gapped frustration-free systems, such as the Affleck-Kennedy-Lieb-Tasaki model and Kitaev's Toric code, have successfully captured universal properties of quantum phases. In contrast, for gapless systems, the assumption of frustration-freeness imposes significant constraints on their phase properties. While typical gapless systems exhibit an emergent Lorentz symmetry with a dynamic critical exponent z = 1, all known examples of gapless frustration-free systems satisfy z ≥ 2. In our study, we rigorously demonstrate, under certain technical assumptions about correlation functions, that the inequality z ≥ 2 holds based on the detectability lemma. This result guarantees the uniqueness of gapless frustration-free systems and establishes a no-go theorem for constructing frustration-free systems with z < 2. Additionally, our findings have important implications for the dynamic universality classes of Markov chain Monte Carlo (MCMC) methods in critical statistical systems. While frustration-free systems might seem artificially constructed, they are in fact common in the context of MCMC. Standard MCMC methods with locality and detailed balance, such as the Metropolis-Hastings algorithm or heat bath methods, can be mapped to frustration-free systems. Our results rigorously prove that for this class of Markov dynamics, the dynamic critical exponent is necessarily z ≥ 2. |
