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arXiv · 2603.26540

Symmetry-resolved properties of the trace distance in thermalizing SU(2) systems

Haojie Shen·Jie Chen·Xiaoqun Wang
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Abstract

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.

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Haojie Shen, Jie Chen, Xiaoqun Wang. 2026-03-27. Symmetry-resolved properties of the trace distance in thermalizing SU(2) systems. https://arxiv.org/abs/2603.26540

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