Abstract The conventional Kibble-Zurek (KZ) mechanism, describing driven dynamics across critical points based on the adiabatic-impulse scenario (AIS), has attracted broad attentions. However, the driven dynamics in the 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 finite-time scaling in which the driving rate has the dimension of r μ = z + 1/ ν μ with z and ν μ 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 p = z + 1/ ν p with ν 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.
Wang et al. (2025) studied this question.