16 Apr 2002 | A. Osterloh(1), L. Amico(1), G. Falci(1), & R. Fazio(2)
This paper discusses the scaling of entanglement near a quantum phase transition, analyzing the properties of concurrence for a class of exactly solvable models in one dimension. It shows that entanglement can be classified within scaling theory and reveals a fundamental difference between classical correlations and quantum entanglement: while classical correlations diverge at the phase transition, entanglement remains short-ranged. The study focuses on a spin-1/2 ferromagnetic chain with exchange coupling J in a transverse magnetic field, and examines the entanglement between two spins in the chain. The results show that entanglement exhibits scaling behavior near the critical point, and that the entanglement between spins is short-ranged, unlike classical correlations. The analysis also shows that the entanglement is not an indicator of the phase transition, but is closely related to scaling and universality. The study demonstrates that the entanglement in the system is governed by the critical exponent ν = 1, consistent with the Ising universality class. The results are relevant for quantum information theory and quantum computation, as they provide insights into the role of entanglement in quantum phase transitions. The paper also discusses the potential applications of these results in quantum computing and error correction.This paper discusses the scaling of entanglement near a quantum phase transition, analyzing the properties of concurrence for a class of exactly solvable models in one dimension. It shows that entanglement can be classified within scaling theory and reveals a fundamental difference between classical correlations and quantum entanglement: while classical correlations diverge at the phase transition, entanglement remains short-ranged. The study focuses on a spin-1/2 ferromagnetic chain with exchange coupling J in a transverse magnetic field, and examines the entanglement between two spins in the chain. The results show that entanglement exhibits scaling behavior near the critical point, and that the entanglement between spins is short-ranged, unlike classical correlations. The analysis also shows that the entanglement is not an indicator of the phase transition, but is closely related to scaling and universality. The study demonstrates that the entanglement in the system is governed by the critical exponent ν = 1, consistent with the Ising universality class. The results are relevant for quantum information theory and quantum computation, as they provide insights into the role of entanglement in quantum phase transitions. The paper also discusses the potential applications of these results in quantum computing and error correction.