Symmetry-resolved properties of the trace distance in thermalizing SU(2) systems
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| Format: | Preprint |
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2026
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| _version_ | 1866910078755405824 |
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| author | Shen, Haojie Chen, Jie Wang, Xiaoqun |
| author_facet | Shen, Haojie Chen, Jie Wang, Xiaoqun |
| contents | We study diagnostics of thermalization in quantum many-body systems with global SU(2) symmetry, where the standard eigenstate thermalization hypothesis (ETH) is generalized to its non-Abelian form. As an eigenstate-level probe, we introduce a symmetry-resolved trace distance constructed from the block structure of the reduced density matrix. This block structure separates spin-sector probabilities from configurational fluctuations within each sector, naturally leading to a decomposition into a probability trace distance and a configurational trace distance. The microcanonical average of the former is bounded by fluctuations of the corresponding spin-sector probabilities within a microcanonical energy window, whereas the latter captures finer intra-sector fluctuations. In non-Abelian thermalizing systems, these spin-sector-probability fluctuations are constrained by the non-Abelian ETH and therefore become exponentially suppressed with system size. Numerical studies of the one-dimensional \(J_1\)--\(J_2\) Heisenberg chain are consistent with this picture and suggest that, in the thermal regime, the trace distance is asymptotically dominated by the configurational trace distance. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_26540 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Symmetry-resolved properties of the trace distance in thermalizing SU(2) systems Shen, Haojie Chen, Jie Wang, Xiaoqun Quantum Physics Statistical Mechanics We study diagnostics of thermalization in quantum many-body systems with global SU(2) symmetry, where the standard eigenstate thermalization hypothesis (ETH) is generalized to its non-Abelian form. As an eigenstate-level probe, we introduce a symmetry-resolved trace distance constructed from the block structure of the reduced density matrix. This block structure separates spin-sector probabilities from configurational fluctuations within each sector, naturally leading to a decomposition into a probability trace distance and a configurational trace distance. The microcanonical average of the former is bounded by fluctuations of the corresponding spin-sector probabilities within a microcanonical energy window, whereas the latter captures finer intra-sector fluctuations. In non-Abelian thermalizing systems, these spin-sector-probability fluctuations are constrained by the non-Abelian ETH and therefore become exponentially suppressed with system size. Numerical studies of the one-dimensional \(J_1\)--\(J_2\) Heisenberg chain are consistent with this picture and suggest that, in the thermal regime, the trace distance is asymptotically dominated by the configurational trace distance. |
| title | Symmetry-resolved properties of the trace distance in thermalizing SU(2) systems |
| topic | Quantum Physics Statistical Mechanics |
| url | https://arxiv.org/abs/2603.26540 |