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This study establishes a fundamental link between periodic-orbit theory and quantum many-body scars within integrable spin chains, offering new microscopic insights into anomalous states that resist thermalization. By demonstrating that these orbital structures persist even when integrability is broken by external fields, the research provides crucial analytical tools for understanding non-equilibrium dynamics in complex quantum systems.
Periodic Orbits Track Quantum States in Integrable Spin Chains
Researchers used the periodic-orbit framework to study the integrable XYZ/XXZ spin-1/2 chain, tracking how these orbits relate to quantum many-body scars and Bethe ansatz solutions.
Researchers at the Institute of Science and Technology Austria (ISTA), Technical University of Munich, and the Munich Center for Quantum Science and Technology have applied the periodic-orbit framework to locate and track periodic orbits within the XYZ/XXZ spin-1/2 chain, an integrable system, revealing a connection to quantum many-body scars. The work demonstrates that zero-momentum magnon pairs surround a common string core within the scarred eigenstates, and their decoupling in the Bethe equations analytically explains the equidistant tower spacing observed in scar phenomenology. This allows for the reconstruction of both scarred eigenstates and associated towers directly within the Bethe ansatz framework, providing a microscopic understanding of these anomalies in an integrable setting. The team, led by Elena Petrova, Maksym Serbyn, and Marko Ljubotina, found this structure persists even when integrability is broken by…
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