Research exposes that while Luttinger’s theorem normally uses to quantum systems, its failure in particular cases links to difficulties in categorizing associated insulators, especially in topological insulators, highlighting a basic connection in between particle habits and quantum matter category. Credit: SciTechDaily.com
In 1960, Luttinger proposed a universal concept linking the overall capability of a system for particles with its reaction to low-energy excitations. Although quickly validated in systems with independent particles, this theorem stays suitable in associated quantum systems defined by extreme inter-particle interactions.
However, and rather remarkably, Luttinger’s theorem has actually been revealed to stop working in really particular and unique circumstances of highly associated stages of matter. The failure of Luttinger’s theorem and its repercussions on the habits of quantum matter are at the core of extreme research study in condensed matter physics.
The Ishikawa-Matsuyama Invariant and Correlated Insulators
Independently of these advancements, essential efforts have actually been devoted to the category and characterization of associated insulating states of matter. In this context, it was revealed that a broad class of topological insulators can be identified by a single integer, called the Ishikawa-Matsuyama invariant, which completely catches its transportation homes.
This result makes up a turning point as it uses an easy prescription for categorizing insulating states in the existence of strong interactions. Very just recently, nevertheless, theorists determined unique designs of associated insulators that inexplicably avoid this attractive category: corrections to the Ishikawa-Matsuyama invariant are therefore needed in strange settings.
Connection Between Luttinger’s Theorem and Insulating State Classification
Writing in the prominent < period class ="glossaryLink" aria-describedby ="tt" data-cmtooltip ="<div class=glossaryItemTitle>Physical Review Letters</div><div class=glossaryItemBody>Physical Review Letters (PRL) is a peer-reviewed scientific journal published by the American Physical Society. It is one of the most prestigious and influential journals in physics, with a high impact factor and a reputation for publishing groundbreaking research in all areas of physics, from particle physics to condensed matter physics and beyond. PRL is known for its rigorous standards and short article format, with a maximum length of four pages, making it an important venue for rapid communication of new findings and ideas in the physics community.</div>" data-gt-translate-attributes="[{"attribute":"data-cmtooltip", "format":"html"}]" tabindex ="0" function ="link" >PhysicalReviewLetters, LucilaPeralta Gavensky andNathanGoldman (ULB), together withSubirSachdev( Harvard), expose that the failure of(*********************************************************************** )’s theorem and the category of insulating states of matter are linked by a basic relation.In essence, these authors show that theIshikawa-Matsuyama invariant completely identifies associated insulators wheneverLuttinger’s theorem is pleased.
In contrast, this topological invariant is revealed to be inadequate to identify correlated stages as quickly as(*********************************************************************** )’s theorem is broken, and the authors supply specific expressions for the needed corrections in regards to appropriate physical amounts.
This essential connection in between Luttinger’s theorem and the topological category of quantum matter clarifies the introduction of unique phenomena in highly associated quantum matter.
Reference: “Connecting the Many-Body Chern Number to Luttinger’s Theorem through Středa’s Formula” by Lucila Peralta Gavensky, Subir Sachdev and Nathan Goldman, 4 December 2023, Physical Review Letters
DOI: 10.1103/ PhysRevLett.131236601
