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

Fuente: arXiv
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Main Authors: Wang, Zhe, Ding, Chengxiang, Liu, Dongxu, Li, Fuxiang, Yan, Zheng, Yin, Shuai
Format: Preprint
Published: 2026
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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
id 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