Magnetic-Field-Induced Insulator-Conductor Transition in $SU(2)$ Quenched Lattice Gauge Theory

We study the correlator of two vector currents in quenched $SU(2)$ 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 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.

Figure 1

The correlator (1) in the confinement (left) and in the deconfinement phases (right) at $T=350\mathrm{MeV}$.

Figure 2

Spectral functions ${\rho }_{ij}(w)$ in the confinement and deconfinement phases.

Figure 3

Electric conductivity of quenched QCD as a function of external magnetic field at different temperatures. The points for ${\sigma }_{zz}$ and ${\sigma }_{xx}$ at $T>T_c$ coincide within the error range.

Figure 4

Electric conductivity in the direction of external magnetic field ${\sigma }_{zz}$ for different lattice parameters.