Tricritical Kibble-Zurek scaling in Rydberg atom ladders

TL;DR

This paper proposes a method to experimentally observe Kibble-Zurek scaling at tricritical points using Rydberg atom ladders, revealing new universal exponents and renormalization group flows beyond standard paradigms.

Contribution

It introduces a protocol for probing tricritical KZ scaling in Rydberg atom arrays, enabling measurement of tricritical exponents and exploring beyond-KZ quantum dynamics.

Findings

Identification of tricritical exponents $ u$ and $ u'$ via ramping protocols.

Observation of renormalization group flows toward second-order critical lines.

Proposal of a measurable emergent spacetime supersymmetry constraint.

Abstract

The Kibble-Zurek (KZ) mechanism has been extensively studied in various second-order phase transitions, yet the case of tricriticality-the point where second-order phase transition lines terminate-remains experimentally elusive. Here, we theoretically propose probing KZ scaling at tricritical points using Rydberg atom arrays arranged as two- and three-leg ladders, which realize the tricritical Ising and tricritical Potts universality classes. By slowly ramping the Rabi frequency and detuning, we extract two relevant tricritical exponents, $\nu$ and $\nu'$, both via conventional paths from the disordered to the ordered phase and via "tangential" paths confined entirely within the disordered phase. At faster speeds, ramping dynamics go beyond the standard KZ paradigm: data collapse analysis using the parent critical exponents (rather than the tricritical ones) reveals renormalization group flows toward the adjacent second-order critical line, and we identify it as a dynamical analog of Zamolodchikov's $c$-theorem. Our protocol is readily implementable on existing Rydberg quantum simulators. This provides a direct route to measuring distinct tricritical exponents which can reveal an emergent spacetime supersymmetry constraint $1/\nu - 1/\nu' = 1$. Moreover, this work deepens our theoretical understanding and opens new avenues for exploring beyond-KZ quantum dynamics with rich renormalization group structure.