Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains

Gabriele De Chiara, Luca Lepori, M. Lewenstein, A. Sanpera

Research output: Contribution to journalLetter

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Abstract

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 ?1, ?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.
Original languageEnglish
Article number237208
Number of pages5
JournalPhysical Review Letters
Volume109
Issue number23
DOIs
Publication statusPublished - 07 Dec 2012

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title = "Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains",
abstract = "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 ?1, ?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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Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains. / De Chiara, Gabriele; Lepori, Luca; Lewenstein, M.; Sanpera, A.

In: Physical Review Letters, Vol. 109, No. 23, 237208, 07.12.2012.

Research output: Contribution to journalLetter

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T1 - Entanglement Spectrum, Critical Exponents and Order Parameters in Quantum Spin Chains

AU - De Chiara, Gabriele

AU - Lepori, Luca

AU - Lewenstein, M.

AU - Sanpera, A.

PY - 2012/12/7

Y1 - 2012/12/7

N2 - 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 ?1, ?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.

AB - 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 ?1, ?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.

U2 - 10.1103/PhysRevLett.109.237208

DO - 10.1103/PhysRevLett.109.237208

M3 - Letter

VL - 109

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 23

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