Real-time chiral dynamics from a digital quantum simulation

Dmitri E Kharzeev,Yuta Kikuchi

doi:10.1103/physrevresearch.2.023342

Abstract

The chiral magnetic effect in a strong magnetic field can be described using the chiral anomaly in the $(1+1)$-dimensional massive Schwinger model with a time-dependent $\theta$-term. We perform a digital quantum simulation of the model at finite $\theta$-angle and vanishing gauge coupling using an IBM-Q digital quantum simulator, and observe the corresponding vector current induced in a system of relativistic fermions by a global {\it chiral quench} -- a sudden change in the chiral chemical potential or $\theta$-angle. At finite fermion mass, there appears an additional contribution to this current that stems from the non-anomalous relaxation of chirality. Our results are relevant for the real-time dynamics of chiral magnetic effect in heavy ion collisions and in chiral materials, as well as for modeling high-energy processes at hadron colliders.

Highlights

Quantum theories possess a multidimensional Hilbert space that becomes very large for relativistic and/or manybody systems
We have considered the behavior of a free model of relativistic fermions under the global chiral quenches that abruptly change the value of the θ angle
This pilot study clarifies the effect of explicit breaking of chiral symmetry by fermion mass on the real-time dynamics of the chiral magnetic effect

Summary

INTRODUCTION

Quantum theories possess a multidimensional Hilbert space that becomes very large for relativistic and/or manybody systems. The chiral magnetic effect (CME) is a generation of electric current in an external magnetic field induced by the chiral asymmetry between the right- and left-handed fermions [41]; see [42,43] for reviews and references. One of the most important effects that determine the real-time dynamics of the CME is the chirality flipping—the transitions between the right- and left-handed fermions that are not related to the anomaly. Since the term describing the nonanomalous chirality flipping in (1) vanishes at m = 0, in this limit of the theory the chiral chemical potential can induce the vector current only at finite fermion mass. We note that the relations (12) and (13) hold for corresponding operators defined on the lattice without taking a continuum limit

Initial state preparation

Evaluation of the vector current

RESULTS AND DISCUSSION

SUMMARY AND OUTLOOK