Disorder-Assisted Adiabaticity in Correlated Many-Particle Systems

Abstract

We investigate how disorder affects adiabaticity in an interacting quantum system by assessing its effect on the state of the system after an interaction modulation, or interaction ``pulse" ,whereby the interaction is changed from zero to a maximum value and then back to zero following a given time profile. We find that, independently of the disorder strength and pulse shapes (rectangular, triangular, and Gaussian), the pulse duration is negatively correlated with the change in total energy in the system. That is, the longer duration reduces the change in total energy for each protocol. Most importantly, across different considered pulse shapes, we find a robust negative correlation between the disorder strength and the change in total energy across the interaction pulse. Namely, increasing the disorder strength systematically suppresses the residual energy added to the system after the interaction pulse, indicating a more adiabatic response. These two effects, disorder-induced and duration-induced adiabaticity, are consistently observed across all three pulse shapes. Among the protocols, the triangular pulse yields the smallest change in total energy in the system over comparable conditions, demonstrating the most adiabatic response. In addition to the energy analysis, we also examine how disorder modifies the effective temperature change across the interaction pulse, to further establish a quantitative relation between disorder and the thermal response. Altogether, our results identify disorder as a key factor in both the energy and the temperature variation over the time-modulation of the interaction.

Figures (12)

• Figure 1: Schematic illustration of the DMFT+CPA solution: (a) Anderson-Hubbard model, electrons can hop between the nearest neighboring lattice sites $i$ and $j$ with hopping amplitude $t_{ij}$, experience an on-site interaction energy $U$ for doubly occupied sites , and are subject to random disorder potential $V_{i}$ (shown as different colors in the figure). (b) Based on DMFT, the disordered lattice is mapped onto a set of disorder configurations on a single impurity site, whose Green’s function is computed by coupling the impurity to an effective bath via a self-consistently determined hybridization function $\Delta(t,t')$. (c) Within the CPA framework, we average over all disorder configurations to obtain the averaged Green’s function $G_{\mathrm{ave}}(t,t')$, which constitutes the DMFT+CPA solution. The self-consistency loop between panels (b) and (c) is iterated until $G_{\mathrm{ave}}(t,t')$ converges.
• Figure 2: The Kadanoff--Baym--Keldysh contour: the system is evolved from an initial time $t_{\min}$ forward to $t_{\max}$, back to $t_{\min}$, and then downward along the imaginary time axis to $t_{\min} - i\beta$. The interaction pulse $U(t)$ start at $t=0$ and end at $t=T_p$, where $T_p$ denotes the pulse duration. The disorder strength $W$ is kept constant throughout the evolution. The real and imaginary-time segments of the contour are discretized using step sizes $\Delta t$ and $\Delta \tau$, respectively.
• Figure 3: Illustration of the relation between the contour-time coordinates $(t, t')$ and the Wigner coordinates $(T_{\mathrm{ave}}, t_{\mathrm{rel}})$ for a point $P$ in the two-time space, where $T_{p}$ denotes the end of the pulse. The pink region indicates the portion of the data that needs to be truncated when evaluating physical quantities in frequency domain after the pulse.
• Figure 4: For the rectangular pulse interaction ($U_{\text{max}}/t^* = 2$, pulse width $T_{\text{p}}$=5), the change in total energy $\Delta E_\text{tot}$ systematically decreases as the disorder strength W increases, indicating that disorder promotes adiabaticity for this sharp on--off driving: (a) Energy as function of time for rectangular pulse interaction with $U_{\text{max}}/t^* = 2$, and pulse width $T_{\text{p}} = 5$ for $W/t* = \; 0.5, \; 1.5, \;2$. The blue, red, and black lines represent the potential, kinetic, and total energy, respectively. (b) $\Delta E_\text{tot}$ vs W for Rectangular Pulse with $U_{\text{max}}/t* = 2$, and pulse width $T_{\text{p}} = 5$. $\Delta E_\text{tot}$ is defined as $E_{\text{tot}}(t_\text{max})-E_{\text{tot}}(t_\text{min})$
• Figure 5: For the Gaussian pulse interaction ($U_{\text{max}}$/t*=2, pulse width $T_{\text{p}}$=12.14), $\Delta E_\text{tot}$ again decreases with increasing disorder. In this smoothly varying protocol, disorder enhances the adiabatic response in agreement with the rectangular and triangular cases: (a) Energy as function of time for Gaussian pulse interaction with $U_{\text{max}}$/t*=2, and pulse width $T_{\text{p}}$=12.14 for W/t*=0.5, 1.5, 2. (b) $\Delta E_\text{tot}$ vs W for gaussian Pulse with $U_{\text{max}}$/t*=2, and pulse width $T_{\text{p}}$=12.14.