Ergodic MPS are the unique frustration-free ground states of parent Hamiltonians that may be infinite-range and need not be gapped.
Periodicity in Ergodic Quantum Processes
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abstract
We study the periodic properties of sequences of quantum channels sampled from an ergodic stochastic process satisfying a natural irreducibility condition. We relate these periodic properties to certain global spectral data defined by the sequence of quantum channels, proving a general Perron-Frobenius-type theorem. We give examples to motivate the theory and conclude with some open problems and conjectures.
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2026 1verdicts
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Parent Hamiltonians of Ergodic Matrix Product States
Ergodic MPS are the unique frustration-free ground states of parent Hamiltonians that may be infinite-range and need not be gapped.