Lieb-Robinson bounds in the continuum via localized frames

• URL: http://arxiv.org/abs/2406.15670v2
• Date: Mon, 22 Jul 2024 18:29:06 GMT
• Title: Lieb-Robinson bounds in the continuum via localized frames
• Authors: Sven Bachmann, Giuseppe De Nittis,
• Abstract summary: We study the dynamics of interacting fermions in the continuum. We first prove a Lieb-Robinson bound that is valid for a general class of local interactions. We then turn to the physical situation relevant to the (fractional) quantum Hall effect.
• Score: 0.27624021966289597
• License: http://creativecommons.org/licenses/by/4.0/
• 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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