Gaussian filters in quantum lattice systems: Applications to spectral flow, local perturbations, clustering, and the quantum Hall effect
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| Format: | Preprint |
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2025
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| _version_ | 1866912548373135360 |
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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 |
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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 |