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arXiv 2602.14599cond-mat.str-el
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非交换动态方法用于具有初始无隙序的Kibble-Zurek缩放极限

Non-commutative Dynamic Approaches to the Kibble-Zurek Scaling Limit with an Initial Gapless Order

Westlake University（西湖大学）；Westlake Institute for Advanced Study（西湖高等研究院）；Anhui University of Technology（安徽工业大学）；Hunan University（湖南大学）；Sun Yat-sen University（中山大学）

Zhe Wang, Chengxiang Ding, Dongxu Liu, Fuxiang Li, Zheng Yan, Shuai Yin

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13 pages, 10 figures
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AI总结：

本研究通过双层海森堡模型揭示了非交换动态特性，表明在特定条件下，Kibble-Zurek缩放极限下的序参量行为受系统尺寸和调谐速率影响，扩展了非平衡缩放理论。

摘要：

非平衡多体物理是现代物理的核心问题之一，而从无隙相到临界点的动态缩放是最重要的挑战之一，目前了解甚少。在跨系统量子临界点（QCP）的驱动动态中，具有大小L的系统，以调谐速率R穿过QCP时，有限时间缩放显示，序参量的平方m²遵循简单的缩放关系m²∝R^{2β/νr}，在Kibble-Zurek（KZ）缩放极限下，RL^r≫1。在这里，通过研究双层海森堡模型中从无隙有序相的驱动临界动态，我们揭示出受KZ缩放极限支配的缩放区域是非交换的：该缩放区域对于大R和有限介质L不可达，而仅在大L和中等有限R时才可达。我们归因于无隙有序相中的有限尺寸修正引起的记忆效应。这种非交换性质使m²仍然强烈依赖于系统尺寸，并且即使对于大R也偏离m²∝R^{2β/νr}。我们进一步表明，类似的修正也适用于虚时间松弛动态。我们的结果确立了非平衡缩放理论在具有无隙有序初始状态方面的本质扩展。

英文摘要：

Nonequilibrium many-body physics is one of the core problems in modern physics, while the dynamical scaling from a gapless phase to the critical point is a most important challenge with very few knowledge so far. In the driven dynamics with a tuning rate $R$ across the quantum critical point (QCP) of a system with size $L$, the finite-time scaling shows that the square of the order parameter $m^2$ obeys a simple scaling relation $m^2\propto R^{2β/νr}$ in the Kibble-Zurek (KZ) scaling limit with $RL^r\gg1$. Here, by studying the driven critical dynamics from a gapless ordered phase in the bilayer Heisenberg model, we unveil that the approaches to the scaling region dominated by the KZ scaling limit with $RL^r\gg1$ are {\it non-commutative}: this scaling region is inaccessible for large $R$ and finite medium $L$, while merely accessible for large $L$ and moderately finite $R$. We attribute this to the memory effect induced by the finite-size correction in the gapless ordered phase. This non-commutative property makes $m^2$ still strongly depends on the system size and deviates from $m^2\propto R^{2β/νr}$ even for large $R$. We further show that a similar correction applies to the imaginary-time relaxation dynamics. Our results establish an essential extension of nonequilibrium scaling theory with a gapless ordered initial state.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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