Gaussian filters in quantum lattice systems: Applications to spectral flow, local perturbations, clustering, and the quantum Hall effect

Fuente: arXiv
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Main Authors: Bachmann, Sven, Zhiqian, Du, Fraas, Martin, Wessel, Tom
Format: Preprint
Published: 2025
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author Bachmann, Sven
Zhiqian
Du
Fraas, Martin
Wessel, Tom
author_facet Bachmann, Sven
Zhiqian
Du
Fraas, Martin
Wessel, Tom
contents We consider the locality and spectral properties of the smearing \[ τ_f(A) = \int_{-\infty}^\infty dt \, f(t) \, τ_t(A) \] when applied to the dynamics $τ_t$ of quantum spin systems. While recent applications of this map have used superpolynomially but not exponentially decaying functions $f$ to ensure exact spectral properties, we use here Gaussian filters. This improves the locality at the expense of errors on the spectral side. We propose a number of concrete applications, from quasi-adiabatic continuation to correlation decay, and exponential stability away from impurities. Finally, we discuss an application to the quantum Hall effect.
format Preprint
id arxiv_https___arxiv_org_abs_2508_15913
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Gaussian filters in quantum lattice systems: Applications to spectral flow, local perturbations, clustering, and the quantum Hall effect
Bachmann, Sven
Zhiqian
Du
Fraas, Martin
Wessel, Tom
Mathematical Physics
Quantum Physics
We consider the locality and spectral properties of the smearing \[ τ_f(A) = \int_{-\infty}^\infty dt \, f(t) \, τ_t(A) \] when applied to the dynamics $τ_t$ of quantum spin systems. While recent applications of this map have used superpolynomially but not exponentially decaying functions $f$ to ensure exact spectral properties, we use here Gaussian filters. This improves the locality at the expense of errors on the spectral side. We propose a number of concrete applications, from quasi-adiabatic continuation to correlation decay, and exponential stability away from impurities. Finally, we discuss an application to the quantum Hall effect.
title Gaussian filters in quantum lattice systems: Applications to spectral flow, local perturbations, clustering, and the quantum Hall effect
topic Mathematical Physics
Quantum Physics
url https://arxiv.org/abs/2508.15913