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Entanglement in a simple quantum phase transition

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arxiv quant-ph/0202162 v1 pith:5KJXUXJG submitted 2002-02-27 quant-ph cond-mat

Tobias J. Osborne , Michael A. Nielsen This is my paper · ORCID
classification quant-phcond-mat
keywords entanglementmodelsystemstransitioncriticaldensityisingmatrix
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What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems which can be solved. An example of such a system is the 1D infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest neighbour entanglement (though not the nearest-neighbour entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behaviour of the entanglement between a single site and the remainder of the lattice.

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Cited by 3 Pith papers

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  1. Multi-entropy and the Dihedral Measures at Quantum Critical Points

    hep-th 2025-06 conditional novelty 7.0 of 10

    The multi-entropy excess κ_2^(3) vanishes for the massless free scalar CFT, an exception to the general c/4 log 2 result, while the Ising model matches it, and new n=3 and n=4 values are proposed for the scalar theory.

  2. Tensor renormalization group approach to entanglement entropy

    hep-lat 2025-09 conditional novelty 6.0 of 10

    A tensor renormalization group algorithm computes entanglement entropy for arbitrary single-interval subsystems and reproduces c=0.49997(8) in the 2D Ising model.

  3. A Breakdown Case Study of the Lindblad Approach via Entanglement and Purity

    quant-ph 2025-07 conditional novelty 5.0 of 10

    A two-qubit system in a random many-body environment decoheres with two successive Gaussian decays, which a time-homogeneous Lindblad equation can never reproduce because its short-time decay is always linear.

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