Magnetic-Field-Induced insulator-conductor transition in SU(2) quenched lattice gauge theory

TL;DR

This study investigates how an external magnetic field affects the electric conductivity in quenched SU(2) lattice gauge theory, revealing a transition from insulator to anisotropic conductor in the confinement phase.

Contribution

It demonstrates that a magnetic field induces electric conductivity along its direction in the confinement phase, a novel insulator-to-conductor transition in lattice gauge theory.

Findings

Magnetic field causes slower decay of current correlator components parallel to the field.

Spectral function analysis shows nonzero conductivity along the magnetic field in the confinement phase.

Conductivity in the deconfinement phase remains unaffected by the magnetic field.

Abstract

We study the correlator of two vector currents in quenched $SU\lr{2}$ lattice gauge theory with a chirally invariant lattice Dirac operator with a constant external magnetic field. It is found that in the confinement phase the correlator of the components of the current parallel to the magnetic field decays much slower than in the absence of a magnetic field, while for other components the correlation length slightly decreases. We apply the maximal entropy method to extract the corresponding spectral function. In the limit of zero frequency this spectral function yields the electric conductivity of the quenched theory. We find that in the confinement phase the external magnetic field induces nonzero electric conductivity along the direction of the field, transforming the system from an insulator into an anisotropic conductor. In the deconfinement phase the conductivity does not exhibit any sizable dependence on the magnetic field.