Lieb–Robinson Bounds in the Continuum Via Localized Frames

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Annales Henri Poincaré Pub Date : 2024-11-16 DOI:10.1007/s00023-024-01511-5

Sven Bachmann, Giuseppe De Nittis

引用次数: 0

Abstract

We study the dynamics of interacting fermions in the continuum. Our approach uses the concept of lattice-localized frames, which we introduce here. We first prove a Lieb-Robinson bound that is valid for a general class of local interactions, which implies the existence of the dynamics at the level of the CAR algebra. We then turn to the physical situation relevant to the (fractional) quantum Hall effect, namely the quasi-free second quantized Landau Hamiltonian to which electron–electron interactions can be added.

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通过定域帧的连续体中的Lieb-Robinson边界

我们研究了连续介质中费米子相互作用的动力学。我们的方法使用格域框架的概念，我们在这里介绍。我们首先证明了对一类一般的局部相互作用有效的Lieb-Robinson界，这意味着在CAR代数水平上存在动力学。然后我们转向与（分数）量子霍尔效应相关的物理情况，即准自由的第二量子化朗道哈密顿量，其中可以添加电子-电子相互作用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.