発表者名 |
政岡 凜太郎 |
指導教員名 |
渡辺 悠樹 准教授 |
発表題目(英語) |
Rigorous lower bound of dynamic critical exponents in critical frustration-free systems
|
要旨(英語) |
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 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 ensures the unique nature of gapless frustration-free systems and establishes a no-go theorem for constructing frustration-free systems with z < 2.
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 z>=2, long recognized but unproven in non-equilibrium statistical physics, finds a rigorous foundation through our quantum framework. |
発表言語 |
日本語 |