2008
DOI: 10.1103/physrevb.78.224402
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Finite-size scaling of string order parameters characterizing the Haldane phase

Abstract: We have developed a numerical procedure to clarify the critical behavior near a quantum phase transition by analyzing a multi-point correlation function characterizing the ground state. This work presents a successful application of this procedure to the string order parameter of the S = 1 XXZ chain with uniaxial single-ion anisotropy. The finite-size string correlation function is estimated by the density matrix renormalization group method. We focus on the gradient of the inversedsystem-size dependence of th… Show more

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Cited by 37 publications
(63 citation statements)
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“…Applying finite-size-scaling analysis [41] allows an accurate location of the corresponding phase-transition lines depicted in Fig. 3 of the main text.…”
Section: Appendix B: Numerical Analysismentioning
confidence: 99%
“…Applying finite-size-scaling analysis [41] allows an accurate location of the corresponding phase-transition lines depicted in Fig. 3 of the main text.…”
Section: Appendix B: Numerical Analysismentioning
confidence: 99%
“…This prediction is supported by conformal field theory arguments 69 and a level spectroscopy method based on a renormalization group analysis and the SU(2)/Z 2 symmetry of the BKT transition 61,[70][71][72] . Numerically, λ 1 ≈ 0 has been verified via finite-size scaling 64,73,74 and DMRG 65 . Finally, at J z = λ 0 = −1, a first-order phase transition from the XY phase to a ferromagnetic Ising phase takes place 61,66,75 .…”
Section: Model Hamiltonian and Phase Diagramsmentioning
confidence: 99%
“…This large systematic error could be reduced using more advanced finite size-scaling methods [35,37], which is beyond the scope of this manuscript. In the inset of Fig.…”
mentioning
confidence: 99%