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

2025/08/21 by Bachmann, Sven, Zhiqian, Du +2
#FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2508.15913

Abstract

We consider the locality and spectral properties of the smearing τ_f(A) = ∫_-∞^∞ 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.

Citations

• BCS Theory in the Weak Magnetic Field Regime for Systems with Nonzero Flux and Exponential Estimates on the Adiabatic Theorem in Extended Quantum Lattice Systems
• Non-equilibrium almost-stationary states and linear response for gapped\n quantum systems
• Lieb-Robinson bounds, Arveson spectrum and Haag-Ruelle scattering theory\n for gapped quantum spin systems
• Locality in Quantum Systems
• Lieb-Robinson Bounds and the Exponential Clustering Theorem

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