Strong-to-weak Symmetry Breaking and Entanglement Transitions
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916636093579264 |
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| author | Chen, Langxuan Sun, Ning Zhang, Pengfei |
| author_facet | Chen, Langxuan Sun, Ning Zhang, Pengfei |
| contents | When interacting with an environment, the entanglement within quantum many-body systems is rapidly transferred to the entanglement between the system and the bath. For systems with a large local Hilbert space dimension, this leads to a first-order entanglement transition for the reduced density matrix of the system. On the other hand, recent studies have introduced a new paradigm for classifying density matrices, with particular focus on scenarios where a strongly symmetric density matrix undergoes spontaneous symmetry breaking to a weak symmetry phase. This is typically characterized by a finite Rényi-2 correlator or a finite Wightman correlator. In this work, we study the entanglement transition from the perspective of strong-to-weak symmetry breaking, using solvable complex Brownian SYK models. We perform analytical calculations for both the early-time and late-time saddles. The results show that while the Rényi-2 correlator indicates a transition from symmetric to symmetry-broken phase, the Wightman correlator becomes finite even in the early-time saddle due to the single-replica limit, demonstrating that the first-order transition occurs between a near-symmetric phase and a deeply symmetry-broken phase in the sense of Wightman correlator. Our results provide a novel viewpoint on the entanglement transition under symmetry constraints and can be readily generalized to systems with repeated measurements. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05364 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong-to-weak Symmetry Breaking and Entanglement Transitions Chen, Langxuan Sun, Ning Zhang, Pengfei Quantum Physics Statistical Mechanics Strongly Correlated Electrons When interacting with an environment, the entanglement within quantum many-body systems is rapidly transferred to the entanglement between the system and the bath. For systems with a large local Hilbert space dimension, this leads to a first-order entanglement transition for the reduced density matrix of the system. On the other hand, recent studies have introduced a new paradigm for classifying density matrices, with particular focus on scenarios where a strongly symmetric density matrix undergoes spontaneous symmetry breaking to a weak symmetry phase. This is typically characterized by a finite Rényi-2 correlator or a finite Wightman correlator. In this work, we study the entanglement transition from the perspective of strong-to-weak symmetry breaking, using solvable complex Brownian SYK models. We perform analytical calculations for both the early-time and late-time saddles. The results show that while the Rényi-2 correlator indicates a transition from symmetric to symmetry-broken phase, the Wightman correlator becomes finite even in the early-time saddle due to the single-replica limit, demonstrating that the first-order transition occurs between a near-symmetric phase and a deeply symmetry-broken phase in the sense of Wightman correlator. Our results provide a novel viewpoint on the entanglement transition under symmetry constraints and can be readily generalized to systems with repeated measurements. |
| title | Strong-to-weak Symmetry Breaking and Entanglement Transitions |
| topic | Quantum Physics Statistical Mechanics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2411.05364 |