Out-of-equilibrium chiral magnetic effect from simulations on Euclidean lattices

Abstract

The status of the chiral magnetic effect (CME) response in full quantum chromodynamics (QCD) has been controversial so far, with previous lattice QCD studies indicating either its strong suppression or vanishing in thermal equilibrium state. We introduce the Euclidean-time correlator of axial charge and electric current as an observable that can be used to study the finite out-of-equilibrium CME response in first-principle lattice QCD simulations with background magnetic field. This observable directly reflects the fact that in the background magnetic field, a state with nonzero axial charge features nonzero electric current. For free fermions, the axial-vector correlator only receives contributions from the lowest Landau level, and exhibits a linear dependence on both magnetic field and temperature with a universal coefficient. With an appropriate regularization, nonvanishing axial-vector correlator is compatible with the vanishing of the CME current in thermal equilibrium state with nonzero chiral chemical potential μ5. We demonstrate that the real-time counterpart of the Euclidean-time axial-vector correlator is intimately related to the real-time form of the axial anomaly equation, which strongly limits possible corrections in full QCD. We present numerical results for the Euclidean-time axial-vector correlator in SU(2) lattice gauge theory with Nf=2 light quark flavors, demonstrating reasonable agreement with free fermion result on both sides of the chiral crossover. The proposed methodology should help to answer the question whether the QCD corrections might be responsible for nonobservation of CME in heavy-ion collision experiments such as the RHIC isobar run. Published by the American Physical Society 2024