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The entanglement entropy of two gapless non-interacting fermion subsystems is computed approximately in a way that avoids the introduction of replicas and a geometric interpretation of the reduced density matrix. We exploit the similarity between the Schmidt basis wavefunction and superfluid BCS wavefunction and compute the entropy using the BCS approximation. Within this analogy, the Cooper pairs are particle-hole pairs straddling the boundary and the effective interaction between them is induced by the projection of the Hilbert space onto the incomplete Schmidt basis. The resulting singular interaction may be thought of as lifting the degeneracy of the single particle distribution function. For two coupled fermion systems of linear size $L$, we solve the BCS gap equation approximately to find the entropy $S approx (w^2/t^2)log{L}$ where $w$ is the hopping amplitude at the boundary of the subsystem and $2t$ is the bandwidth. We further interpret this result based upon the relationship between entanglement spectrum, entropy and number fluctuations.
Starting from a state of low quantum entanglement, local unitary time evolution increases the entanglement of a quantum many-body system. In contrast, local projective measurements disentangle degrees of freedom and decrease entanglement. We study th
We formulate a new ``Wigner characteristics based method to calculate entanglement entropies of subsystems of Fermions using Keldysh field theory. This bypasses the requirements of working with complicated manifolds for calculating R{e}nyi entropies
We discuss the behavior of the entanglement entropy of the ground state in various collective systems. Results for general quadratic two-mode boson models are given, yielding the relation between quantum phase transitions of the system (signaled by a
We consider scaling of the entanglement entropy across a topological quantum phase transition in one dimension. The change of the topology manifests itself in a sub-leading term, which scales as $L^{-1/alpha}$ with the size of the subsystem $L$, here
We study the entanglement entropy of blocks of contiguous spins in non-periodic (quasi-periodic or more generally aperiodic) critical Heisenberg, XX and quantum Ising spin chains, e.g. in Fibonacci chains. For marginal and relevant aperiodic modulati