Two-Point Entanglement Near a Quantum Phase Transition

Details Two-Point Entanglement Near a Quantum Phase Transition Two-Point Entanglement Near a Quantum Phase Transition

2006-06-05

arxiv.org/abs/cond-mat/0606126v3

J. Phys. A: Math. Theor. 40 (2007) 10215-10224

Physics

Condensed Matter

Statistical Mechanics

published version

Scientific paper

10.1088/1751-8113/40/33/017

In this work, we study the two-point entanglement S(i,j), which measures the entanglement between two separated degrees of freedom (ij) and the rest of system, near a quantum phase transition. Away from the critical point, S(i,j) saturates with a characteristic length scale $\xi_E$, as the distance |i-j| increases. The entanglement length $\xi_E$ agrees with the correlation length. The universality and finite size scaling of entanglement are demonstrated in a class of exactly solvable one dimensional spin model. By connecting the two-point entanglement to correlation functions in the long range limit, we argue that the prediction power of a two-point entanglement is universal as long as the two involved points are separated far enough.

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