Quantum Mpemba effect in quasiperiodic systems

TL;DR

This work investigates relaxation dynamics and steady-state transitions in a one-dimensional quasiperiodic tight-binding model with simultaneous diagonal and off-diagonal modulations. Using ${\rm MIPR}$ and fractal-dimension analysis, it maps the equilibrium phase diagram, identifying extended, critical, and localized regimes with an elliptical boundary approximately satisfying $\sqrt{V^{2}/4 + t_{1}^{2}} = t$. It then introduces quasiperiodic bond dissipation within a Lindblad framework ($L_n = c^{\dagger}_n c_{n+\ell}$, $\gamma_n = \gamma \cos(2\pi \alpha n)$) to obtain non-equilibrium steady-state phase diagrams, revealing dissipation-induced delocalization-localization transitions and reentrant behavior as parameters vary. The paper further demonstrates a quantum Mpemba effect via trace-distance dynamics $d_{\rm Tr}$, where localized or critical initial states can relax faster than states closer in energy to the steady state, explained by a starting-line hypothesis based on center-of-mass displacements $\Delta x_{\rm com}$. Overall, the results advance understanding of steady-state phase transitions and relaxation in dissipatively driven quasiperiodic systems and point to experimental possibilities in optical lattices and related platforms.

Abstract

We study a one-dimensional quasiperiodic tight-binding model with simultaneous off-diagonal (hopping) and diagonal (onsite) modulations. Using the inverse participation ratio and the wave-packet centroid, we construct localization-delocalization phase diagrams for both equilibrium and nonequilibrium steady states. We analyze the robustness of initial-state properties under dissipation and characterize dissipation-induced localization-delocalization transitions (and their reversals) in detail. Trace-distance dynamics provide evidence for a quantum Mpemba effect: states prepared farther from the steady state can relax faster than states initialized closer to it. We propose a starting-line hypothesis that explains the presence or absence of this effect across parameter regimes. These results advance the understanding of steady-state phase transitions and relaxation dynamics in dissipatively driven quasiperiodic systems.

Figures (4)

• Figure 1: (Color Online) The phase diagram illustrates how $\log_{10}(\rm MIPR)$ varies with $V/t$ and $t_{1}/t$, where the system size is set to $L = 1597$. The red dashed line represents the phase boundary, which serves to distinguish the extended phase from the localized and critical phases. Meanwhile, the colorbar corresponds to the numerical values of $\log_{10}(\rm MIPR)$.
• Figure 2: (Color Online) (a) $\log_{10}(\rm MIPR)$ as a function of $r$ with $\theta=0$, $\pi/4$, $\pi/3$, and $5\pi/6$. (b) $\overline{D_{min}}$ as a function of the inverse Fibonacci index $1/m$ under different $(r,\theta)$.
• Figure 3: (Color Online) Steady state phase diagram. (a) $V=0$. (b) $V=0.5t$. (c) $V=t$. (d) $V=2t$. The blue regions denote the delocalization phases. The yellow regions denote the localization phases. Other parameter is $L=100$.
• Figure 4: (Color Online) Trace distance $d_{\rm Tr}$ versus evolution time $\tau$. (a) $V=0$, $t_{1}=1.2t$, and $\gamma=0.5t$. (b) $V=0$, $t_{1}=1.7t$, and $\gamma=0.8t$. (c) $V=0.2t$, $t_{1}=1.2t$, and $\gamma=0.2t$. (d) $V=0.2t$, $t_{1}=1.5t$, and $\gamma=0.2t$. (e) $V=0.2t$, $t_{1}=0.8t$, $\gamma=0.2t$. (f) $V=0.5t$, $t_{1}=0.5t$, $\gamma=0.2t$. The ordinal number in the caption indicates the ordinal number of the initial state in the eigenstates of $H$. Other parameter is $L=100$.