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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.14923 |
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| _version_ | 1866910035041320960 |
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| author | Kaur, Manmeet Bhattacharjee, Somendra M. |
| author_facet | Kaur, Manmeet Bhattacharjee, Somendra M. |
| contents | Dynamical quantum phase transitions (DQPTs) are a class of non-equilibrium phase transitions that occur in many-body quantum systems during real-time evolution, rather than through parameter tuning as in conventional phase transitions. This paper presents an exact analytical approach to studying DQPTs by combining complex dynamics with the real-space renormalization group (RG). RG transformations are interpreted as iterated maps on the complex plane, establishing a connection between DQPTs and the Julia set, the boundary separating the basins of attraction of the stable fixed points. This framework is applied to a quantum quench in the one-dimensional transverse field Ising model, where we examine the sensitivity of DQPTs to variations in boundary conditions. We show that altering the topology of the spin chain can suppress DQPTs and provide a qualitative explanation based on quantum speed limits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14923 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Julia Set in Quantum Evolution: The case of Dynamical Quantum Phase Transitions Kaur, Manmeet Bhattacharjee, Somendra M. Statistical Mechanics Quantum Physics Dynamical quantum phase transitions (DQPTs) are a class of non-equilibrium phase transitions that occur in many-body quantum systems during real-time evolution, rather than through parameter tuning as in conventional phase transitions. This paper presents an exact analytical approach to studying DQPTs by combining complex dynamics with the real-space renormalization group (RG). RG transformations are interpreted as iterated maps on the complex plane, establishing a connection between DQPTs and the Julia set, the boundary separating the basins of attraction of the stable fixed points. This framework is applied to a quantum quench in the one-dimensional transverse field Ising model, where we examine the sensitivity of DQPTs to variations in boundary conditions. We show that altering the topology of the spin chain can suppress DQPTs and provide a qualitative explanation based on quantum speed limits. |
| title | Julia Set in Quantum Evolution: The case of Dynamical Quantum Phase Transitions |
| topic | Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2509.14923 |