[论文解读] Disorder-Assisted Adiabaticity in Correlated Many-Particle Systems

S. H. Liou, Herbert F. Fotso|arXiv (Cornell University)|Mar 10, 2026

Spectroscopy and Quantum Chemical Studies被引用 0

一句话总结

研究表明，在无序相互作用系统（Anderson–Hubbard 模型）中，更强的无序以及更长/更软的相互作用脉冲降低剩余能量和有效温度的变化，促进在不同脉冲形状下的绝热演化。

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.

研究动机与目标

• 理解无序如何影响强相关系统的非平衡态下的绝热性。
• 研究带有无序的 Anderson–Hubbard 模型中相互作用脉冲对能量与温度的影响。
• 探索脉冲形状和持续时间如何影响矩形、三角形和高斯型脉冲下的绝热性。
• 使用非平衡 DMFT+CPA 框架同时处理相互作用与无序。
• 在脉冲后量化残余能量和有效温度，以将无序、脉冲持续时间和脉冲形状与绝热性联系起来。

提出的方法

• 模型：在 Bethe 晶格上的带有 U(t) 脉冲和在[-W, W]均匀分布的无序 V_i 的系统。
• 求解：非平衡 DMFT+CPA，求解不纯粒子格林函数 G_Vi(t,t') 并对无序取平均得到 G_ave(t,t')。
• 不纯粒子求解器：二阶扰动理论给出 Sigma_Vi(t,t') = -U(t)U(t') G_Vi(t,t')^2 G_Vi(t',t)。
• 自洽：Delta(t,t') = t*^2 G_ave(t,t') 在无限维 Bethe 晶格上。
• 观测量：动能、势能和总能量 E_kin, E_pot, E_tot，以及通过涨落-耗散定理和费米-狄拉克拟合得到的有效温度。
• 考虑的脉冲：矩形、三角形和高斯型，具有相同总面积（U_max、T_p，以及在文中定义的轮廓）。
• 分析：在脉冲后跟踪残余能量 Delta E_tot，并通过涨落-耗散关系从 G^<(omega) 中提取 beta_final。

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 di

实验结果

研究问题

• RQ1 无序强度 W 如何影响 Anderson–Hubbard 模型中相互作用脉冲后的残余能量？
• RQ2 在固定 U_max、改变 T_p 的情况下，矩形、三角形、高斯脉冲形状对绝热性有何影响？
• RQ3 脉冲持续时间对在不同无序强度下的能量吸收和加热有何作用？
• RQ4 无序如何影响相互作用调制过程中的有效温度变化？

主要发现

• 增加的无序强度系统地抑制脉冲后的残余总能量，指示更具绝热性的响应。
• 更长的脉冲持续时间在所有脉冲形状下降低总能量的变化。
• 在脉冲形状中，三角脉冲产生了最小的 Delta E_tot，显示出最强的绝热响应。
• 无序和脉冲持续时间都促进绝热性，在中等到强值时无序往往占主导。
• 有效的最终温度变化与能量变化相关联，并且被更强的无序和更长的脉冲所降低，三角脉冲产生的温度变化最小。
• 在所有脉冲形状中，无序在相互作用调制过程中持续降低能量和温度的变化。

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 $T_{p}$ deno