Kibble-Zurek Mechanism in the Open Quantum Rabi Model

Abstract

The Kibble-Zurek mechanism provides a universal framework for predicting defect formation in non-equilibrium phase transitions. While Markovian dissipation typically degrades universal scaling, the impact of non-Markovian memory remains largely unexplored. We demonstrate that an Ohmic bath induces a Berezinskii-Kosterlitz-Thouless transition in the open quantum Rabi model. Using simulations based on Matrix Product States, we show that the excitation energy strictly follows universal Kibble-Zurek power-law scaling when evaluated at the freeze-out time. Crucially, we find that since the environment defines the universality class, dissipation does not inherently compete with adiabatic dynamics, in stark contrast to Markovian regimes. Our results establish the Kibble- Zurek mechanism as a robust witness of universality in open quantum systems, revealing that non-Markovian memory preserves the integrity of non-equilibrium scaling.

Figures (6)

• Figure 1: Relaxation time $\tau$ vs $g/\Delta$: numerical data (black dots) and fit to the BKT scaling $\tau \propto \exp[B/\sqrt{g_c - g}]$ (solid red line), yielding $g_c/\Delta \simeq 0.918$.
• Figure 2: Freeze-out time $t_f$ (a) and excitation energy $E_{\mathrm{exc}}$ (b) vs $g/\Delta$. (a) Intersection of the BKT relaxation time $\tau(g)$ (dashed line) and the quench-induced residual time $t_r(g)$ (solid lines) for various $t_Q$: red dots denote the freeze-out time identification. (b) $E_{\mathrm{exc}}$ for different quench rates: red dots mark the breakdown of adiabaticity, with the shaded area indicating the numerically unreliable regime for $g > 0.8$.
• Figure 3: Excitation energy $E_{\mathrm{exc}}/\Delta$ (a) and excitation probability $P_{\mathrm{exc}}$ (b) vs $t_f\Delta$. (a) Power-law scaling of the residual energy: black dots denote numerical data, solid red line indicates the algebraic fit $\propto t_f^{-0.992}$. (b) Excitation probability scaling: solid red line marks the corresponding fit $\propto t_f^{-0.074}$.
• Figure 4: Estimated excitation energy $E_{\mathrm{exc}}/\Delta$ (a) and scaling collapse (b) vs $t_f\Delta$. (a) Estimated energy $P_{\mathrm{exc}}\Delta_{\mathrm{eff}}$ (dots) and power-law fit $\propto t_f^{-1.074}$ (solid line). (b) Measured $E_{\mathrm{exc}}$ (black dots) and $P_{\mathrm{exc}}\Delta_{\mathrm{eff}}$ rescaled to the first data point (red squares); the overlap confirms that both quantities share the same scaling behavior, differing only by a multiplicative factor.
• Figure 5: Relaxation dynamics of $\Sigma_z(t)$ in the OQRM. (a) Coherent oscillations at weak coupling. (b) Crossover to critically damped behavior near the Toulouse point. (c) Strictly overdamped regime approaching the quantum critical point. Couplings $g/\Delta$ are indicated in each panel.