Kibble-Zurek behavior in a topological phase transition with a quadratic band crossing
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| Format: | Preprint |
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2024
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| _version_ | 1866929548943163392 |
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| author | Yuan, Huan Zhang, Jinyi Chen, Shuai Nie, Xiaotian |
| author_facet | Yuan, Huan Zhang, Jinyi Chen, Shuai Nie, Xiaotian |
| contents | Kibble-Zurek (KZ) mechanism describes the scaling behavior when driving a system across a continuous symmetry-breaking transition. Previous studies have shown that the KZ-like scaling behavior also lies in the topological transitions in the Qi-Wu-Zhang model (2D) and the Su-Schrieffer-Heeger model (1D), although symmetry breaking does not exist here. Both models with linear band crossings give that $ν=1$ and $z=1$. We wonder whether different critical exponents can be acquired in topological transitions beyond linear band crossing. In this work, we look into the KZ behavior in a topological 2D checkerboard lattice with a quadratic band crossing. We investigate from dual perspectives: momentum distribution of the Berry curvature in clean systems for simplicity, and real-space analysis of domain-like local Chern marker configurations in disordered systems, which is a more intuitive analog to conventional KZ description. In equilibrium, we find the correlation length diverges with a power $ν\simeq 1/2$. Then, by slowly quenching the system across the topological phase transition, we find that the freeze-out time $t_\mathrm{f}$ and the unfrozen length scale $ξ(t_\mathrm{f})$ both satisfy the KZ scaling, verifying $z\simeq 2$. We subsequently explore KZ behavior in topological phase transitions with other higher-order band crossing and find the relationship between the critical exponents and the order. Our results extend the understanding of the KZ mechanism and non-equilibrium topological phase transitions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_19780 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kibble-Zurek behavior in a topological phase transition with a quadratic band crossing Yuan, Huan Zhang, Jinyi Chen, Shuai Nie, Xiaotian Statistical Mechanics Disordered Systems and Neural Networks Quantum Gases Strongly Correlated Electrons Quantum Physics Kibble-Zurek (KZ) mechanism describes the scaling behavior when driving a system across a continuous symmetry-breaking transition. Previous studies have shown that the KZ-like scaling behavior also lies in the topological transitions in the Qi-Wu-Zhang model (2D) and the Su-Schrieffer-Heeger model (1D), although symmetry breaking does not exist here. Both models with linear band crossings give that $ν=1$ and $z=1$. We wonder whether different critical exponents can be acquired in topological transitions beyond linear band crossing. In this work, we look into the KZ behavior in a topological 2D checkerboard lattice with a quadratic band crossing. We investigate from dual perspectives: momentum distribution of the Berry curvature in clean systems for simplicity, and real-space analysis of domain-like local Chern marker configurations in disordered systems, which is a more intuitive analog to conventional KZ description. In equilibrium, we find the correlation length diverges with a power $ν\simeq 1/2$. Then, by slowly quenching the system across the topological phase transition, we find that the freeze-out time $t_\mathrm{f}$ and the unfrozen length scale $ξ(t_\mathrm{f})$ both satisfy the KZ scaling, verifying $z\simeq 2$. We subsequently explore KZ behavior in topological phase transitions with other higher-order band crossing and find the relationship between the critical exponents and the order. Our results extend the understanding of the KZ mechanism and non-equilibrium topological phase transitions. |
| title | Kibble-Zurek behavior in a topological phase transition with a quadratic band crossing |
| topic | Statistical Mechanics Disordered Systems and Neural Networks Quantum Gases Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2407.19780 |