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      Entanglement in XY Spin Chain

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          Abstract

          We consider the ground state of the XY model on an infinite chain at zero temperature. Following Bennett, Bernstein, Popescu, and Schumacher we use entropy of a sub-system as a measure of entanglement. Vidal, Latorre, Rico and Kitaev conjectured that von Neumann entropy of a large block of neighboring spins approaches a constant as the size of the block increases. We evaluated this limiting entropy as a function of anisotropy and transverse magnetic field. We used the methods based on integrable Fredholm operators and Riemann-Hilbert problem. The entropy is singular at phase transitions.

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          Quantum information and computation

          In information processing, as in physics, our classical world view provides an incomplete approximation to an underlying quantum reality. Quantum effects like interference and entanglement play no direct role in conventional information processing, but they can--in principle now, but probably eventually in practice--be harnessed to break codes, create unbreakable codes, and speed up otherwise intractable computations.
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            Scaling of Entanglement close to a Quantum Phase Transitions

            , , (2002)
            In this Letter we discuss the entanglement near a quantum phase transition by analyzing the properties of the concurrence for a class of exactly solvable models in one dimension. We find that entanglement can be classified in the framework of scaling theory. Further, we reveal a profound difference between classical correlations and the non-local quantum correlation, entanglement: the correlation length diverges at the phase transition, whereas entanglement in general remains short ranged.
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              Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent

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                Author and article information

                Journal
                2004-09-03
                2004-10-22
                Article
                10.1088/0305-4470/38/13/011
                quant-ph/0409027
                a9ec7d72-dd9b-4e78-9a25-898d33cb270a
                History
                Custom metadata
                YITP-SB-04-47
                Journal Phys. A: Math. Gen. vol 38, pages 2975-2990, 2005
                8 pages and 2 figures
                quant-ph cond-mat.stat-mech nlin.SI

                Quantum physics & Field theory
                Quantum physics & Field theory

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