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Entanglement and quantum criticality in spin chains

X. X. Yi, H. T. Cui, L. C. Wang

Published Nov 3, 2005• 0 citations
OpenAlex

Abstract

A relation between entanglement and criticality of spin chains is established. The entanglement we exploit is shared between auxiliary particles, which are isolated from each other, but are coupled to the same critical spin-1/2 chain. We analytically evaluate the reduced density matrix, and numerically show the entanglement of the auxiliary particles in the proximity of the critical points of the spin chain. We find that the entanglement induced by a critical many-body system may reach one, and it can signal very well the critical points of the spin chain. A physical understanding and experimental realization with trapped ions are presented.

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We investigate the entanglement spectrum near criticality in finite quantum spin chains. Using finite size scaling we show that when approaching a quantum phase transition, the Schmidt gap, i.e., the difference between the two largest eigenvalues of the reduced density matrix λ(1), λ(2), signals the critical point and scales with universal critical exponents related to the relevant operators of the corresponding perturbed conformal field theory describing the critical point. Such scaling behavior allows us to identify explicitly the Schmidt gap as a local order parameter.
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