On dynamic critical exponents of gapless frustration-free systems
Frustration-free systems are theoretically tractable quantum systems characterized by ground states that minimize all local terms in the Hamiltonian simultaneously. For gapped phases, frustration-free systems have been successful as models that approximate general systems. 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 , all known examples of gapless frustration-free systems satisfy . This suggests that frustration-freeness can be used to classify gapless quantum phases.
In this talk, we present a proof of for dynamic critical exponents for gapless frustration-free systems, assuming certain technical conditions on correlation functions. We will illustrate this result with several examples of gapless frustration-free systems, highlighting the implications of their anomalous dynamic critical exponents.
Additionally, we discuss the notable connection between frustration-free systems and Markov processes. It is known that Markov processes which describe standard relaxation to equilibrium states can be mapped onto frustration-free systems. The inequality , long recognized but unproven in non-equilibrium statistical physics, finds a rigorous foundation through our quantum framework.
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