Proves exact separability for disconnected subsystems in dimer RK states and exponentially suppressed entanglement for RVB states on arbitrary lattices, with negativity expressed via partition functions.
Entanglement negativity in quantum field theory
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abstract
We develop a systematic method to extract the negativity in the ground state of a 1+1 dimensional relativistic quantum field theory, using a path integral formalism to construct the partial transpose rho_A^{T_2} of the reduced density matrix of a subsystem A=A1 U A2, and introducing a replica approach to obtain its trace norm which gives the logarithmic negativity E=ln||\rho_A^{T_2}||. This is shown to reproduce standard results for a pure state. We then apply this method to conformal field theories, deriving the result E\sim(c/4) ln(L1 L2/(L1+L2)) for the case of two adjacent intervals of lengths L1, L2 in an infinite system, where c is the central charge. For two disjoint intervals it depends only on the harmonic ratio of the four end points and so is manifestly scale invariant. We check our findings against exact numerical results in the harmonic chain.
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Third-order negativity is a necessary and sufficient criterion for full separability of tripartite pure states and extends to mixed states and qudits.
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Separability and entanglement of resonating valence-bond states
Proves exact separability for disconnected subsystems in dimer RK states and exponentially suppressed entanglement for RVB states on arbitrary lattices, with negativity expressed via partition functions.
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Separability from Multipartite Measures
Third-order negativity is a necessary and sufficient criterion for full separability of tripartite pure states and extends to mixed states and qudits.