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Lieb-Robinson causality and non-Fermi liquids

Subham Dutta Chowdhury and Aditya Hebbar

Sean A. Hartnoll

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Phys. Rev. B 113, 245125 – Published 12 June, 2026

DOI: https://doi.org/10.1103/1q5b-3w57

Abstract

Quantum mechanical lattice models with local, bounded interactions obey Lieb-Robinson causality. We show that this implies a domain of analyticity of the retarded Green's function GR(ω,k) of local lattice operators as a function of complex frequency ω and momentum k, similar to the light-cone analyticity property of relativistic field theories. Low-energy effective descriptions of the dynamics must be consistent with this microscopic analyticity constraint. We consider two canonical low-energy fermionic Green's functions describing non-Fermi liquids, the marginal Fermi liquid and the ‘‘Hertz liquid.’’ The pole in these Green's functions must be outside of the Lieb-Robinson domain of analyticity for all complex momenta captured by the low-energy theory. This constraint upper bounds the magnitude of the dimensionless non-Fermi-liquid coupling in certain Hertz liquids.

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Phys. Rev. B 113, 245125– Published 12 June, 2026
  • Received 3 December 2025
  • Accepted 18 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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