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arXiv · 2508.15913

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

Sven Bachmann·Zhiqian·Du·Martin Fraas·Tom Wessel
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Abstract

We consider the locality and spectral properties of the smearing \[ \tau_f(A) = \int_{-\infty}^\infty dt \, f(t) \, \tau_t(A) \] when applied to the dynamics $\tau_t$ 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.

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Sven Bachmann, Zhiqian, Du, Martin Fraas, Tom Wessel. 2025-08-21. Gaussian filters in quantum lattice systems: Applications to spectral flow, local perturbations, clustering, and the quantum Hall effect. https://arxiv.org/abs/2508.15913

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