Quantum Anomaly and Thermodynamics of One-Dimensional Fermions with Three-Body Interactions

Area of Science:

• Quantum mechanics
• Condensed matter physics
• Many-body systems

Background:

• Two-dimensional (2D) fermions with two-body contact interactions are well-studied and exhibit a scale anomaly.
• Nonrelativistic systems with contact interactions are generally not expected to display scale anomalies.

Purpose of the Study:

• To investigate the phenomenon of scale anomaly in one-dimensional (1D) systems.
• To explore the connection between scale anomalies in 1D and 2D fermionic systems.
• To analyze the thermodynamic properties of 1D fermionic systems with three-body interactions.

Main Methods:

• Theoretical analysis of a three-species, one-dimensional Fermi gas with attractive three-body contact interactions.
• Calculation of the equation of state and pressure at finite temperatures.
• Generalization of Tan's contact to three-body forces.

Main Results:

• A scale anomaly is identified in the 1D three-body fermion system, directly linked to the anomaly in 2D two-body systems.
• This 1D system and its 2D counterpart are identified as the sole nonrelativistic contact-interaction systems exhibiting a scale anomaly.
• The impact of the anomaly on the equation of state and pressure is calculated for the 1D system.
• The third-order virial coefficient is found to be proportional to the second-order coefficient of the 2D two-body case.

Conclusions:

• The study establishes a novel connection between scale anomalies in 1D and 2D fermionic systems.
• It provides a theoretical framework for understanding and calculating thermodynamic properties in unexplored 1D systems.
• The findings suggest that scale anomalies in contact-interacting Fermi gases are rare and specific to these 1D and 2D configurations.