Energy space entanglement spectrum of pairing models with s-wave and p-wave symmetry

Abstract

Entanglement between blocks of energy-levels is analysed for systems exhibiting s-wave and p-wave superconductivity. We study the entanglement entropy and spectrum of a block of $\ell$ levels around the Fermi point, and also between particles and holes, in the ground state of Richardson-type Hamiltonians. The maximal entropy grows with the number of levels $L$ approximately as $1/2\log (L)$, as suggested by the permutational symmetry of the state at large coupling. The number of levels in the block around the Fermi surface with maximal entanglement is proposed as a measure of the number of {\em active Cooper pairs}, which correlates with standard estimates of this magnitude. The entanglement spectrum is always composed of a principal parabolic band plus {\em higher bands} whose disappearance signals a exact BCS state, e.g. in the Moore-Read line, while the Read-Green quantum phase transition is characterized by a maximum in their weight.

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Cited by in corpus (3)

• An integrable case of the p+ip pairing Hamiltonian interacting with its environment
• Exact solution of the p+ip Hamiltonian revisited: duality relations in the hole-pair picture
• Fourier-space entanglement of spin chains