Magnetic-Field-Induced Insulator-Conductor Transition inSU(2)Quenched Lattice Gauge Theory

Abstract

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 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.PACS numbers: 11.30. Rd; 12.38.Gc; Recently, heavy ion experiments at the BNL Relativistic Heavy Ion Collider (RHIC) have found an evidence [1] for the so-called chiral magnetic effect [2] in quarkgluon plasma. The essence of the effect is the generation of electric current along the direction of the external magnetic field in the background of topologically nontrivial gauge field configurations. Experimentally, the effect manifests itself as the dynamical enhancement of fluctuations in the numbers of charged hadrons emitted above and below the reaction plane in off-central heavyion collisions. Recently this effect has been studied also in lattice gauge theory, and the evidence for charge separation in magnetic field has been found [3,5]. In [3] it has been found that the fluctuations of the electric current along the magnetic field are strongly enhanced as compared to the fluctuations of current in the perpendicular directions. This conclusion was also confirmed by an analytical calculation in the instanton gas model [6]. The result of [3] on the difference of longitudinal and transverse electric current susceptibilities has been reproduced later by an analytical calculation [7]; the frequency dependence of the conductivity has also been evaluatedfor the weak coupling result, see [8].A natural question to ask is whether this enhancement of current fluctuations corresponds to a real flow of charge, or is just caused by short-lived quantum fluctuations. This question can be answered by studying the current-current correlation functions. The currents which correspond to a real transport of charged particles should have long-range correlations in time, while quantum fluctuations are typically characterized by a finite correlation time [9]. Recalling Green-Kubo relations, one can see that this property is intimately related to the electric conductivity -namely, the real transport of charged particles can occur only in conducting media.

Anomalies and time reversal invariance in relativistic hydrodynamics: The second order and higher dimensional formulations

“…[9,10,11] for recent discussions on this), the origin of the effect is essentially topological and so the CME is not renormalized even at strong coupling, as was shown by the holographic methods [12,13,14,15,16,17,18]. The evidence for the CME has been found in lattice QCD coupled to electromagnetism, both within the quenched approximation [19,20,21] and with light domain wall fermions [22]. Unlike the baryon chemical potential, the chiral chemical potential µ A does not present a "sign problem" which opens a possibility for lattice computations at finite µ A [4].…”

In memory of Mikhail Igorevich Polikarpov

“…In [17] it was found that indeed magnetic field strongly enhances the fluctuations of electric current in the direction of the magnetic field. In [18] this enhancement was related to the emergence of electric conductivity in the direction of magnetic field. It was predicted that this phenomenon should manifest itself in specific anisotropy of the distribution of soft leptons produced in heavy-ion collisions.…”

Shear viscosity η to electrical conductivity σel ratio for an anisotropic QGP

“…It is of fundamental importance for the strength of chiral magnetic effect [44], a signature of CP-violation of the strong interaction. Recently, electric conductivity has been studied by different groups [30,31,[45][46][47][48][49][50][51][54][55][56][57][58][59]. It is related to the soft dilepton production rate [60] and the magnetic field diffusion in the medium [61,62].…”