Translation-covariant disordered spin states with finite correlations are shown to admit disordered matrix product decompositions on Banach bundles, and an IID-sampled AKLT state is proven gapless yet exponentially clustering with Tasaki index -1.
Matrix Product States as Observations of Entangled Hidden Markov Models
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abstract
This paper reveals the intrinsic structure of Matrix Product States (MPS) by establishing their deep connection to entangled hidden Markov models (EHMMs). It is demonstrated that a significant class of MPS can be derived as the outcomes of EHMMs, showcasing their underlying quantum correlations. Additionally, a lower bound is derived for the relative entropy between the EHMM-observation process and the corresponding MPS, providing a quantitative measure of their informational divergence. Conversely, it is shown that every MPS is naturally associated with an EHMM, further highlighting the interplay between these frameworks. These results are supported by illustrative examples from quantum information, emphasizing their importance in understanding entanglement, quantum correlations, and tensor network representations.
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Finitely Correlated States Driven by Topological Dynamics
Translation-covariant disordered spin states with finite correlations are shown to admit disordered matrix product decompositions on Banach bundles, and an IID-sampled AKLT state is proven gapless yet exponentially clustering with Tasaki index -1.