• anderson
• field
• lattice
• localization
• magnetic
• qcd
• qft

Localization appears in Condensed Matter and low-energy fermionic states when Dirac fermions are coupled to the QCD non-Abelian SU(3) gauge fields. The mobility edge separates localized and delocalized modes in the spectrum, and it's an order parameter for the Anderson transition. As temperature drops, the mobility edge approaches zero. When it hits a specific point, localized modes vanish, and eigenmodes become completely delocalized.
I studied the statistical properties of the spectrum of rooted staggered fermions with an improved Symanzik gauge action. Rational Hybrid Monte Carlo algorithm is used to sample gauge links in the Path Integral formalism in the presence of an external magnetic field B applied as a U(1) constant phase in the xy plane.
To analyze the transition from Poissonian independent distributed spacings to Gaussian Unitary Ensemble distribution, I used the Unfolded Level Spacing Distribution (ULSD) and the Integrated ULSD. The participation ratio provides a quantitative assessment of the extent to which an eigenstate is distributed over the lattice volume.
A non-perfectly Poissonian distribution in the lower part of the spectrum suggests that the magnetic field may affect the vacuum structure. Topological charges were analyzed in gauge configurations, smoothed using the Cooling algorithm to remove UV fluctuations. This influence may lead to partially overlapping eigenstates, altering their behavior.