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Crosscap states with tunable entanglement as exact eigenstates of local spin chain Hamiltonians
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Crosscap states with tunable entanglement as exact eigenstates of local spin chain Hamiltonians
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It has been observed recently that various spin chain Hamiltonians admit special zero energy "crosscap" eigenstates. These states are made up of maximally entangled Bell pairs prepared on antipodal sites of a periodic chain. We generalize the states by allowing the antipodal pairs to have non-maximal, tunable entanglement. We give sufficient conditions for such states to be exact zero energy eigenstates of a local Hamiltonian. The conditions are naturally satisfied in many models which have a global U(1) symmetry. These models include well known integrable models such as the XX model, the Bariev model, the folded XXZ model, and also a variety of non-integrable models. Using the zero-energy crosscap states we also derive a family of exact zero modes with sub-volume law entanglement.
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Solving models with generalized free fermions I: Algebras and eigenstates
Spin chains with hidden free-fermion structure acquire explicit exact eigenstates through an anti-symmetric combination of two commuting Hamiltonian copies, demonstrated for the free-fermions-in-disguise model.
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