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/2. In particular it is possible that the space S will not be invariant under translation by one site (notice, however, that if T is the translation by one site, the subspace S is explicitly invariant under T2).
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/ 2. In particular it is possible that the space S will not be invariant under translation by one site (notice, however, that if T is the translation by one site, the subspace S is explicitly invariant under T 2).
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n) with a pure state |ψ (n) obtained by coherently superimposing all its translated versions. On the base of "ultraviolet catastrophe" arguments, we can indeed argue that, in the thermodynamical limit, the statistics associated with any local observable will be identical in the two cases.
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Notice that such averaging needs not be performed in a classical fashion (i.e., by replacing the state | ψ (n) with a mixture of all possible translations of the same vector). Instead, the same average can be performed in a coherent fashion by replacing | ψ (n) with a pure state | ψ (n) obtained by coherently superimposing all its translated versions. On the base of "ultraviolet catastrophe" arguments, we can indeed argue that, in the thermodynamical limit, the statistics associated with any local observable will be identical in the two cases.
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