Scaling of the Schmidt gap in the vicinity of a critical point

Seminar date and time: 
Friday, 9 March, 2012 - 11:00
Anna Sanpera
IFAE seminar room (UAB)

We investigate both, analytically and numerically, by means of the density matrix renormalization group (DMRG) algorithm, the discrete part of the entanglement spectrum at criticality and near criticality for finite quantum spin chains. Using finite size scaling analysis we show that the Schmidt gap, i.e. the difference between the two largest eigenvalues of the reduced density matrix λ1 , λ2 , scales with universal critical exponents when approaching a quantum phase transition and signals the critical point. Moreover, our results allows to identify the Schmidt gap explicitly as a local order parameter if the corresponding critical point is described by a Conformal Field Theory with a single relevant operator.

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