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The entanglement spectrum in many-body ultracold bosonic gases


We investigate quantum phases with spinor bosonic gases using quantum information tools.  We show that in finite quantum spin chains when approaching a quantum phase transition, the Schmidt gap, i.e. the difference between the two largest eigenvalues of the reduced density matrix $\lambda_{1},\lambda_{{2}}$, signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding conformal theory describing the perturbation from the critical point. Such scaling behavior allows to identify explicitly the Schmidt gap as a local order parameter.