Topological Bound on the Structure Factor.

Area of Science:

• Condensed matter physics
• Quantum many-body theory
• Topological phases of matter

Background:

• Topological phases of matter exhibit unique properties determined by topology, often characterized by quantized responses.
• Understanding the fundamental properties and constraints of these phases is crucial for developing new quantum technologies.
• Many-body systems with U(1) symmetry are prevalent in condensed matter, including superconductors and quantum Hall states.

Purpose of the Study:

• To establish a fundamental lower bound for the static structure factor in general many-body systems with U(1) symmetry.
• To demonstrate the universality of this bound across various two-dimensional gapped topological phases.
• To uncover new universal features of topological phases beyond conventional quantized responses.

Main Methods:

• Derivation of a lower bound for the static structure factor using principles of causality and non-negative energy dissipation.
• Application of the derived bound to specific topological phases, including (fractional) Chern insulators, (fractional) quantum spin Hall insulators, topological superconductors, and chiral spin liquids.
• Analysis of the implications of the bound for understanding topological order.

Main Results:

• A universal lower bound for the static structure factor of U(1) symmetric many-body systems has been identified.
• This lower bound is solely determined by the ground state Chern number.
• The bound is valid for a broad class of two-dimensional gapped systems, including various topological phases.

Conclusions:

• The study reveals a novel universal feature of topological phases, extending beyond quantized responses.
• The derived lower bound provides a new perspective on the fundamental properties of topological matter.
• The findings offer a powerful tool for characterizing and understanding diverse topological states of matter.