Non-commutative Dynamic Approaches to the Kibble-Zurek Scaling Limit with an Initial Gapless Order
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| Format: | Preprint |
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2026
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| _version_ | 1866917275829796864 |
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| author | Wang, Zhe Ding, Chengxiang Liu, Dongxu Li, Fuxiang Yan, Zheng Yin, Shuai |
| author_facet | Wang, Zhe Ding, Chengxiang Liu, Dongxu Li, Fuxiang Yan, Zheng Yin, Shuai |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_14599 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-commutative Dynamic Approaches to the Kibble-Zurek Scaling Limit with an Initial Gapless Order Wang, Zhe Ding, Chengxiang Liu, Dongxu Li, Fuxiang Yan, Zheng Yin, Shuai Strongly Correlated Electrons 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. |
| title | Non-commutative Dynamic Approaches to the Kibble-Zurek Scaling Limit with an Initial Gapless Order |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2602.14599 |