Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866917948159950848 |
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| author | Lessa, Leonardo A. Ma, Ruochen Zhang, Jian-Hao Bi, Zhen Cheng, Meng Wang, Chong |
| author_facet | Lessa, Leonardo A. Ma, Ruochen Zhang, Jian-Hao Bi, Zhen Cheng, Meng Wang, Chong |
| contents | Symmetry in mixed quantum states can manifest in two distinct forms: strong symmetry, where each individual pure state in the quantum ensemble is symmetric with the same charge, and weak symmetry, which applies only to the entire ensemble. This paper explores a novel type of spontaneous symmetry breaking (SSB) where a strong symmetry is broken to a weak one. While the SSB of a weak symmetry is measured by the long-ranged two-point correlation function, the strong-to-weak SSB (SW-SSB) is measured by the fidelity correlator. We prove that SW-SSB is a universal property of mixed-state quantum phases, in the sense that the phenomenon of SW-SSB is robust against symmetric low-depth local quantum channels. We also show that the symmetry breaking is "spontaneous" in the sense that the effect of a local symmetry-breaking measurement cannot be recovered locally. We argue that a thermal state at a nonzero temperature in the canonical ensemble (with fixed symmetry charge) should have spontaneously broken strong symmetry. Additionally, we study non-thermal scenarios where decoherence induces SW-SSB, leading to phase transitions described by classical statistical models with bond randomness. In particular, the SW-SSB transition of a decohered Ising model can be viewed as the "ungauged" version of the celebrated toric code decodability transition. We confirm that, in the decohered Ising model, the SW-SSB transition defined by the fidelity correlator is the only physical transition in terms of channel recoverability. We also comment on other (inequivalent) definitions of SW-SSB, through correlation functions with higher Renyi indices. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_03639 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States Lessa, Leonardo A. Ma, Ruochen Zhang, Jian-Hao Bi, Zhen Cheng, Meng Wang, Chong Quantum Physics Mesoscale and Nanoscale Physics Strongly Correlated Electrons Symmetry in mixed quantum states can manifest in two distinct forms: strong symmetry, where each individual pure state in the quantum ensemble is symmetric with the same charge, and weak symmetry, which applies only to the entire ensemble. This paper explores a novel type of spontaneous symmetry breaking (SSB) where a strong symmetry is broken to a weak one. While the SSB of a weak symmetry is measured by the long-ranged two-point correlation function, the strong-to-weak SSB (SW-SSB) is measured by the fidelity correlator. We prove that SW-SSB is a universal property of mixed-state quantum phases, in the sense that the phenomenon of SW-SSB is robust against symmetric low-depth local quantum channels. We also show that the symmetry breaking is "spontaneous" in the sense that the effect of a local symmetry-breaking measurement cannot be recovered locally. We argue that a thermal state at a nonzero temperature in the canonical ensemble (with fixed symmetry charge) should have spontaneously broken strong symmetry. Additionally, we study non-thermal scenarios where decoherence induces SW-SSB, leading to phase transitions described by classical statistical models with bond randomness. In particular, the SW-SSB transition of a decohered Ising model can be viewed as the "ungauged" version of the celebrated toric code decodability transition. We confirm that, in the decohered Ising model, the SW-SSB transition defined by the fidelity correlator is the only physical transition in terms of channel recoverability. We also comment on other (inequivalent) definitions of SW-SSB, through correlation functions with higher Renyi indices. |
| title | Strong-to-Weak Spontaneous Symmetry Breaking in Mixed Quantum States |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2405.03639 |