Under the Extended Uncertainty Principle, position variance saturates, and the entanglement entropy of harmonic chains and massless scalar fields saturates to a finite value with a discrete, evenly gapped entanglement spectrum.
How universal is the entanglement spectrum?
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It is now commonly believed that the ground state entanglement spectrum (ES) exhibits universal features characteristic of a given phase. In this letter, we show that this belief is false in general. Most significantly, we show that the entanglement Hamiltonian can undergo quantum phase transitions in which its ground state and low energy spectrum exhibit singular changes, even when the physical system remains in the same phase. For broken symmetry problems, this implies that the ES and the Renyi entropies can mislead entirely, while for quantum Hall systems the ES has much less universal content than assumed to date.
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Resolution of Infrared Entanglement Divergences via the Extended Uncertainty Principle
Under the Extended Uncertainty Principle, position variance saturates, and the entanglement entropy of harmonic chains and massless scalar fields saturates to a finite value with a discrete, evenly gapped entanglement spectrum.