Spin-fermion model near the quantum critical point: one-loop renormalization group results

Area of Science:

• Condensed Matter Physics
• Quantum Materials
• Statistical Mechanics

Background:

• Itinerant electron systems near antiferromagnetic critical points exhibit complex spin and electronic behaviors.
• Previous studies were limited to the N = infinity approximation, neglecting crucial finite-size effects.

Purpose of the Study:

• To investigate spin and electronic properties of itinerant electron systems beyond the N = infinity limit.
• To identify new physical effects arising from finite hot spot numbers in the Brillouin zone.

Main Methods:

• Utilized the spin-fermion model to describe the system.
• Performed an expansion in the inverse number of hot spots (1/N) in the Brillouin zone.
• Calculated corrections to first order in 1/N.

Main Results:

• Discovered Fermi surface nesting at hot spots, a previously unobserved phenomenon.
• Identified anomalous spin dynamics due to vertex corrections.
• Found that vertex corrections modify the dynamical critical exponent from z = 2 to z > 2.
• Derived a new expression for the critical exponent: z = 2N/(N-2), yielding z ≈ 2.67 for N = 8.

Conclusions:

• The study reveals significant deviations from the N = infinity limit in itinerant electron systems.
• Finite hot spot numbers and vertex corrections are crucial for understanding anomalous spin dynamics and critical phenomena.