Driven Critical Dynamics in Tricitical Point

TL;DR

This paper investigates the driven critical dynamics at a one-dimensional supersymmetric Ising tricritical point, revealing how Kibble-Zurek scaling applies in multiple directions with different critical exponents.

Contribution

It introduces a novel analysis of nonequilibrium dynamics at a tricritical point with two relevant directions, extending Kibble-Zurek theory beyond conventional critical points.

Findings

Kibble-Zurek scaling applies along the Ising critical line with a specific driving rate dimension.

Different directions at the tricritical point have distinct critical exponents affecting the dynamics.

The study provides a new perspective on nonequilibrium critical phenomena near tricritical points.

Abstract

The conventional Kibble-Zurek (KZ) mechanism, describing driven dynamics across critical points based on the adiabatic-impulse scenario (AIS), have attracted broad attentions. However, the driven dynamics in tricritical point with two independent relevant directions has not been adequately studied. Here, we employ time dependent variational principle to study the driven critical dynamics at a one-dimensional supersymmetric Ising tricritical point. For the relevant direction along the Ising critical line, the AIS apparently breaks down. Nevertheless, we find that the critical dynamics can still be described by the KZ scaling in which the driving rate has the dimension of $r=z+1/\nu_\mu$ with $z$ and $\nu_\mu$ being the dynamic exponent and correlation length exponent in this direction, respectively. For driven dynamics along other direction, the driving rate has the dimension $r=z+1/\nu_p$ with $\nu_p$ being the other correlation length exponent. Our work brings new fundamental perspective into the nonequilibrium critical dynamics near the tricritical point, which could be realized in programmable quantum processors in Rydberg atomic systems.