ResearchPod Summary
In standard quantum systems, thermal noise acts as a destructive force that rapidly suppresses entanglement, typically limiting it to short-range correlations that vanish in the thermodynamic limit. This paper investigates whether a strong non-Abelian conservation law—a constraint that restricts dynamics to a specific symmetry sector—can fundamentally alter this behavior and allow thermal states to host macroscopic, system-size-diverging entanglement.
The author examines finite-range SU(2)-invariant spin chains restricted to the global-singlet sector. By employing a representation-space protocol, the study analyzes how local thermal fluctuations within these chains map onto subsystem spin fluctuations. The author uses a combination of quantum belief propagation, linked-cluster expansions for twisted partition functions, and exact diagonalization of nonintegrable chains to track how these fluctuations scale with the system size N.
The study demonstrates that non-Abelian conservation laws force the thermal state to occupy irreducible representations of dimension proportional to the square root of the system size. This geometric constraint converts local thermal noise into a robust, operational resource. Specifically, the distillable entanglement across a macroscopic bipartition scales as 1/2 log2(N) plus a constant term, even at high temperatures. An exactly solvable dimer chain model confirms this, showing that while the zero-temperature state is unentangled, any finite temperature activates this logarithmic entanglement. Numerical tests on nonintegrable chains confirm that this scaling persists beyond solvable models.
This work identifies a qualitative divide between Abelian and non-Abelian constraints in quantum many-body systems. While Abelian symmetries can sometimes preserve entanglement, they often fail to prevent it from vanishing in the thermodynamic limit. In contrast, non-Abelian symmetries define a distinct thermal-resource regime where heating acts as an activator for long-range entanglement. This provides a new mechanism for generating and maintaining quantum resources in thermal environments, with potential implications for quantum information processing and the study of thermalization in constrained systems.
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