Real-time dynamics of Chern-Simons fluctuations near a critical point

Kazuki Ikeda,Dmitri E Kharzeev,Yuta Kikuchi

doi:10.1103/physrevd.103.l071502

Kazuki Ikeda, Dmitri E Kharzeev + Show 1 more

Open Access

https://doi.org/10.1103/physrevd.103.l071502

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Abstract

The real-time topological susceptibility is studied in $(1+1)$-dimensional massive Schwinger model with a $\ensuremath{\theta}$-term. We evaluate the real-time correlation function of electric field that represents the topological Chern-Pontryagin number density in ($1+1$) dimensions. Near the parity-breaking critical point located at $\ensuremath{\theta}=\ensuremath{\pi}$ and fermion mass $m$ to coupling $g$ ratio of $m/g\ensuremath{\approx}0.33$, we observe a sharp maximum in the topological susceptibility. We interpret this maximum in terms of the growth of critical fluctuations near the critical point, and draw analogies between the massive Schwinger model, QCD near the critical point, and ferroelectrics near the Curie point.

Highlights

The Schwinger model [1] is quantum electrodynamics in ð1 þ 1Þ space-time dimensions
The real-time topological susceptibility is studied in ð1 þ 1Þ-dimensional massive Schwinger model with a θ-term
We interpret this maximum in terms of the growth of critical fluctuations near the critical point, and draw analogies between the massive Schwinger model, QCD near the critical point, and ferroelectrics near the Curie point

Summary

INTRODUCTION

The Schwinger model [1] is quantum electrodynamics in ð1 þ 1Þ space-time dimensions. For massless fermions, the Schwinger model is analytically solvable and equivalent to the theory of a free massive boson field [1,2,3,4,5,6,7,8]; the model with massive fermions presents a challenge for analytical methods and has a rich dynamics. The massive Schwinger model possesses a quantum phase transition at θ 1⁄4 π between the phases with opposite orientations of the electric field, see Fig. 1. Coleman [59] that the line of the first order phase transition terminates at some critical value mÃ, where the phase transition is second order Ψ → eiγ5θψ and ψ → ψeiγ5θ, the action is transformed to,1 It is clear from (2) that the massive theory with a positive mass m > 0 at θ 1⁄4 π is equivalent to the theory at θ 1⁄4 0 but with a negative mass −m

TOPOLOGICAL FLUCTUATIONS NEAR THE CRITICAL POINT

Lattice Hamiltonian

Real-time topological susceptibility

RESULTS AND DISCUSSION