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• W1982113704 endingPage "P02008" @default.
• W1982113704 startingPage "P02008" @default.
• W1982113704 abstract "We report on a systematic approach for the calculation of the negativity in the ground state of a one-dimensional quantum field theory. The partial transpose rho_A^{T_2} of the reduced density matrix of a subsystem A=A_1 U A_2 is explicitly constructed as an imaginary-time path integral and from this the replicated traces Tr (rho_A^{T_2})^n are obtained. The logarithmic negativity E= log||rho_A^{T_2}|| is then the continuation to n->1 of the traces of the even powers. For pure states, this procedure reproduces the known results. We then apply this method to conformally invariant field theories in several different physical situations for infinite and finite systems and without or with boundaries. In particular, in the case of two adjacent intervals of lengths L1, L2 in an infinite system, we derive the result Esim(c/4) ln(L1 L2/(L1+L2)), where c is the central charge. For the more complicated case of two disjoint intervals, we show that the negativity depends only on the harmonic ratio of the four end-points and so is manifestly scale invariant. We explicitly calculate the scale-invariant functions for the replicated traces in the case of the CFT for the free compactified boson, but we have not so far been able to obtain the n->1 continuation for the negativity even in the limit of large compactification radius. We have checked all our findings against exact numerical results for the harmonic chain which is described by a non-compactified free boson." @default.
• W1982113704 created "2016-06-24" @default.
• W1982113704 creator A5004177676 @default.
• W1982113704 creator A5008391443 @default.
• W1982113704 creator A5076249507 @default.
• W1982113704 date "2013-02-01" @default.
• W1982113704 modified "2023-10-17" @default.
• W1982113704 title "Entanglement negativity in extended systems: a field theoretical approach" @default.
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• W1982113704 doi "https://doi.org/10.1088/1742-5468/2013/02/p02008" @default.
• W1982113704 hasPublicationYear "2013" @default.
• W1982113704 type Work @default.
• W1982113704 sameAs 1982113704 @default.

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