Lieb-Schultz-Mattis Constraints for Quantum Channels: A Spacetime-Duality View

• URL: http://arxiv.org/abs/2608.26266v1
• Date: Wed, 26 Aug 2026 18:00:07 GMT
• Title: Lieb-Schultz-Mattis Constraints for Quantum Channels: A Spacetime-Duality View
• Abstract summary: We show how LSM constraints shape dynamical signatures and temporal correlations in open quantum systems.<n>We identify the textitLiouvillian singular spectrum as a more fundamental diagnostic of quantum anomalies.
• Score: 2.5787427887880283
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum anomalies strongly constrain the possible behavior of many-body systems. A prime example is the Lieb-Schultz-Mattis (LSM) theorem, which relates UV symmetry and filling constraints to IR features of the energy spectrum and ground-state structure. Here, we ask how LSM constraints shape dynamical signatures and temporal correlations in open quantum systems. Using a spacetime duality, we show that the Liouvillian of a $d$-dimensional repeated quantum channel with a mixed anomaly between strong $S$ and weak $G$ symmetry can be mapped to a $(d{+}1)$-dimensional mixed-state symmetry-protected topological (mSPT) phase. Under this correspondence, the initial and steady states of the channel are identified with boundary states of the higher-dimensional mSPT in the presence of bulk projection. We further introduce the twisted Renyi-$N$ correlator (TRNC) as a probe of temporal correlations in the channel and demonstrate that it is dual to the mSPT strange correlator, providing a direct bulk-boundary route to diagnose long-range temporal order implied by the LSM anomaly. Finally, we identify the \textit{Liouvillian singular spectrum}, rather than the Liouvillian spectrum itself, as a more fundamental diagnostic of quantum anomalies, and show that it is dual to the operator entanglement spectrum of the mSPT.

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