Luttinger Count is the Homotopy Not the Physical Charge: Generalized Anomalies Characterize Non-Fermi Liquids

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory

Background:

• The Luttinger-Ward functional is crucial for understanding interacting electron systems.
• Deviations from simple Fermi liquid theory, like in non-Fermi liquids, require advanced theoretical frameworks.

Purpose of the Study:

• To reformulate the Luttinger-Ward functional within path integral formalism.
• To establish a connection between generalized symmetries, quantized charges, and anomalies.
• To provide a classification scheme for non-Fermi liquids.

Main Methods:

• Formulation of the Luttinger-Ward functional as an operator insertion in the path integral.
• Analysis of divergences in the functional and zeros of the Green's function.
• Application of triangle-diagram anomaly concepts.

Main Results:

• The Luttinger-Ward functional can be interpreted as a generalized symmetry.
• Quantized charges associated with this symmetry relate to homotopy, distinct from physical charge.
• Divergences lead to triangle-type anomalies, explaining Luttinger count deviations.
• Non-Fermi liquids can be classified using established particle physics anomaly structures.

Conclusions:

• Generalized symmetries, arising from functional divergences, yield nonlocal charges with distinct experimental signatures.
• The study offers a new perspective on non-Fermi liquids through the lens of quantum field theory anomalies.
• This framework unifies the understanding of charge quantization and anomalous phenomena in condensed matter.