Interacting fermions in two dimensions: beyond the perturbation theory

Area of Science:

• Condensed Matter Physics
• Quantum Many-Body Systems
• Low-Dimensional Systems

Background:

• Standard perturbation theory is often used to study interacting fermion systems.
• However, its applicability can be limited in certain regimes, such as low dimensions.
• The behavior of two-dimensional (2D) fermion systems with short-range interactions presents unique challenges.

Purpose of the Study:

• To investigate the limitations of perturbation theory for 2D fermions with short-range interactions.
• To identify the source of divergences in the perturbative series for the self-energy.
• To develop a more accurate description of the fermion self-energy and spectral function.

Main Methods:

• Analysis of a 2D fermion system with short-range interactions.
• Application of perturbation theory and identification of its divergences near the mass shell.
• Resummation of the most divergent diagrams to obtain a closed-form self-energy.
• Calculation of the spectral function and analysis of specific heat.

Main Results:

• Perturbation theory is ill-defined even for weak interactions due to divergences in the self-energy series.
• These divergences arise from the interaction of fermions with the zero-sound collective mode.
• A closed-form self-energy is derived by resumming divergent diagrams.
• The spectral function shows a threshold feature related to zero-sound emission.
• The T^2 specific heat remains unaffected by zero-sound interactions.

Conclusions:

• The interaction with zero sound fundamentally alters the behavior of 2D fermions, invalidating simple perturbation theory.
• A new theoretical framework is established for describing the self-energy and spectral properties of these systems.
• The findings provide insights into collective excitations and their impact on thermodynamic properties in 2D fermionic matter.