Conformal magnetic effect at the edge: A numerical study in scalar QED

M.N Chernodub,V.A Goy,A.V Molochkov

doi:10.1016/j.physletb.2019.01.003

Abstract

Quantum polarization effects associated with the conformal anomaly in a static magnetic field background may generate a transverse electric current in the vacuum. The current may be produced either in an unbounded curved spacetime or in a flat spacetime in a physically bounded system. In both cases, the magnitude of the electric current is proportional to the beta-function associated with renormalization of the electric charge. In our article, we investigate the electric current density induced by the magnetic field in the vicinity of a Dirichlet boundary in the scalar QED. Using first-principle lattice simulations we show that the electric current, generated by this “conformal magnetic effect at the edge” (CMEE), is well described by the conformal anomaly provided the conformal symmetry is classically unbroken. Outside of the conformal limit, the current density is characterized by an anomalous power law near the edge of the system and by an exponential suppression of the current far away from the edge.

Highlights

Quantum anomalies lead to a large variety of unusual transport phenomena such as the chiral magnetic effect [1], the chiral vortical effect [2] and their generalizations [3]
In was recently proposed that the scale magnetic effect may be realized in Dirac and Weyl semimetals as a Nernst effect, i.e. the generation of an anomalous electric current normal to a temperature gradient that drives the system slightly out of equilibrium [6]
In our paper we numerically investigate, from the first principles, the generation of the boundary electric current in the lattice formulation of the (3+1) dimensional Abelian Higgs model (AHM) following the analytical studies of Refs. [8, 9]

Summary

Introduction

Quantum anomalies lead to a large variety of unusual transport phenomena such as the chiral magnetic effect [1], the chiral vortical effect [2] and their generalizations [3]. In the presence of the background magnetic field the conformal anomaly may generate an electric current in spatially bounded systems [8, 9]. In our paper we numerically investigate, from the first principles, the generation of the boundary electric current in the lattice formulation of the (3+1) dimensional Abelian Higgs model (AHM) following the analytical studies of Refs. The electric current at the boundary (1) is proportional to the beta function associated with the renormalization of electric charge via Eq (2), highlighting the conformal–anomalous nature of this Conformal magnetic edge effect (CMEE). In order to numerically simulate the theory (8) we employ the lattice Abelian Higgs model (AHM) with a certain potential on the scalar field, and search for the conformal point where both scalar and gauge fields become (almost) massless as in Eq (8). A direct calculation at the conformal point is rather challenging due to large correlation lengths which require time-consuming simulations at large volumes

Conformal point

Electric current

Findings

Conclusions