Entanglement-limited linear response in fermionic systems

TL;DR

This paper establishes a direct link between entanglement entropy scaling laws and the linear response functions in fermionic systems, revealing how entanglement influences physical responses like energy absorption and fluctuations.

Contribution

It introduces a general connection between entanglement entropy and linear response in particle-conserving fermionic ground states, verified across various entanglement regimes.

Findings

Response to perturbations scales with entanglement entropy

Energy absorption in gapped systems scales with boundary, not volume

Response functions are governed by entanglement properties

Abstract

We propose a general connection between entanglement-entropy scaling laws and the linear response functions of particle-conserving fermionic systems in their ground state. Specifically, we show that the response to perturbations coupled to the particle number within a finite region exhibits the same size scaling as the entanglement entropy of that region. We explicitly verify this scaling in free-fermion systems that display area-law, volume-law, and critical forms of entanglement. The resulting entanglement-governed scaling of response functions leads to unexpected physical consequences. For instance, contrary to conventional expectations, the energy absorption rate and particle-number fluctuations in gapped systems scale with the boundary of the perturbed region rather than with its volume. Our work thus establishes a direct link between linear-response properties and many-body entanglement.