Topological bound on structure factor

TL;DR

This paper establishes a universal lower bound on the static structure factor in many-body systems with $U(1)$ symmetry, linking it to the ground state Chern number, and applies it across various topological phases.

Contribution

It introduces a topological bound on the structure factor based solely on causality and dissipation, applicable to diverse topological systems.

Findings

Lower bound depends only on ground state Chern number

Bound applies to fractional and non-fractional topological phases

Universal feature of topological phases beyond quantized responses

Abstract

We show that the static structure factor of general many-body systems with $U(1)$ symmetry has a lower bound determined only by the ground state Chern number. Our bound relies only on causality and non-negative energy dissipation, and holds for a wide range of systems. We apply our theory to (fractional) Chern insulators, (fractional) quantum spin Hall insulators, topological superconductors, and chiral spin liquids. Our results uncover a universal feature of topological phases beyond the quantized response.