From black hole to one-dimensional chain: parity symmetry breaking and kink formation

TL;DR

This paper models kink formation in a strongly coupled one-dimensional system using AdS/CFT correspondence, revealing universal scaling laws and statistical properties of kinks during symmetry-breaking phase transitions.

Contribution

It introduces a novel holographic model for discrete parity symmetry breaking and kink formation, extending the AdS/CFT framework beyond continuous symmetry breaking.

Findings

Kink hairs form in the bulk due to parity symmetry breaking.

The dual kink number follows a universal power-law with quench rate.

Higher cumulants of kink numbers are proportional to the mean, indicating binomial distribution.

Abstract

AdS/CFT correspondence is a "first-principle" tool to study the strongly coupled many-body systems. While it has been extensively applied to investigate the continuous symmetry breaking dynamics, the discrete symmetry breaking dynamics are rarely investigated. In this paper, the model of kink formation in a strongly coupled one-dimensional chain is realized from the AdS/CFT correspondence. In doing so, we first construct a model of real scalar fields with parity symmetries in the AdS bulk. By quenching the system across the critical point at a finite rate, kink hairs turn out in the bulk due to the spontaneous parity symmetry breaking, which accomplishes a counter-example of "no hair conjecture" of black hole. Due to the AdS/CFT correspondence, kink hairs in the bulk are dual to the kinks in the AdS boundary. The mean of the dual kink numbers are found to satisfy a universal power-law relation to the quench rate, in agreement with the celebrated Kibble-Zurek mechanism. Moreover, the higher cumulants of the kink numbers are proportional to the mean numbers, consistent with the assumption that the formation of kinks satisfy the binomial distributions which goes beyond the Kibble-Zurek mechanism.