統計物理学メーリングリストのみなさま、
東大物性研の川畑です。
以下のとおり、政岡凜太郎さんのセミナーを開催します。
関心のあるかたは、
https://www.issp.u-tokyo.ac.jp/maincontents/seminar/all2.html?ptype=seminar&pid=25487
から参加登録してくださると幸いです。
よろしくお願いいたします。
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日時：2024 年 12 月 20 日（金）16:00-17:00
場所：東京大学物性研究所 A615 および Zoom（ハイブリッド開催）
講師：政岡凜太郎（東大・物工）
タイトル：On dynamic critical exponents of gapless frustration-free systems
概要：
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 z = 1, all known examples of gapless frustration-free
systems satisfy z >= 2. This suggests that frustration-freeness can be used
to classify gapless quantum phases.
In this talk, we present a proof of z >= 2 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 z>=2, long recognized but unproven
in non-equilibrium statistical physics, finds a rigorous foundation through
our quantum framework.
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川畑 幸平
東京大学 物性研究所
E-mail: kawabata [at] issp.u-tokyo.ac.jp