Disorder-Driven Quantum Transition in Relativistic Semimetals: Functional Renormalization via the Porous Medium...

Area of Science:

• Condensed Matter Physics
• Quantum Phase Transitions
• Disordered Systems

Background:

• Relativistic semimetals exhibit quantum transitions to diffusive phases under randomness.
• The U(N) Gross-Neveu model (N→0) is a standard but incomplete approach to these transitions.
• Gaussian approximations neglect crucial fluctuations.

Purpose of the Study:

• To investigate quantum transitions in relativistic semimetals beyond standard models.
• To develop a method incorporating beyond-Gaussian fluctuations.
• To identify the true nature of the critical fixed point and associated phenomena.

Main Methods:

• Utilized a functional renormalization group (fRG) method.
• Incorporated fluctuations beyond the Gaussian approximation.
• Analyzed the renormalization of disorder distribution via the porous medium equation.

Main Results:

• Identified an infinitely unstable fixed point in the standard U(N) Gross-Neveu model.
• Revealed a novel, nonanalytic fixed point governing the transition.
• Demonstrated spontaneous generation of a finite density of states.
• Characterized scaling behavior of broad fluctuation distributions.

Conclusions:

• The standard U(N) Gross-Neveu model is insufficient for describing these transitions.
• A functional renormalization group approach reveals a new critical behavior.
• The findings offer insights into spontaneous state generation and fluctuation scaling.
• The methodology is applicable to other nonanalytic phenomena like Anderson localization.