Erratum: Numerical-diagonalization study of spin gap issue of the kagome lattice heisenberg antiferromagnet (Journal of the Physical Society of Japan (2011) 80 (053704) DOI: 10.1143/JPSJ.80.053704);Numerical-diagonalization study of spin gap issue of the kagome lattice heisenberg antiferromagnet

Journal of the Physical Society of Japan

Volumn 80, Issue 5, 2011, Pages

  Nakano, Hiroki ^a   Sakai, Toru ^b  

^a UNIVERSITY OF HYOGO   (Japan)

^b JAPAN ATOMIC ENERGY AGENCY   (Japan)

Author keywords

Antiferromagnetic Heisenberg spin model; Frustration; Kagome lattice; Lanczos method; Numerical diagonalization method

Indexed keywords

EID: 79956116070     PISSN: 00319015     EISSN: 13474073     Source Type: Journal    
DOI: 10.7566/JPSJ.90.038002     Document Type: Erratum

References (25)

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13. The case of the largest dimension, namely, Ns = 42 and M = 0, has taken approximately 680 s per Lanczos step in an MPI-parallelized job with 8192 processes in SGI Altix ICE 8400EX, ISSP, University of Tokyo. The case of Ns = 39 and M = 1/2 has taken about 139 s per Lanczos step in a hybrid parallel job with 512 processes by 16 threads in Hitachi SR16000, Department of Simulation Science, NIFS.
14. This hybrid code was developed originally in the study of the precise estimate of the Haldane gap in ref. 15.
15. H. Nakano and A. Terai: J. Phys. Soc. Jpn. 78 (2009) 014003.
16. The record before the present study was 159 059 993 400 in the study of the two-dimensional doped Hubbard model in refs. 17 and 18.
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19. In Fig. 13 of ref. 1, the linear fitting of a mixture of data of even Ns and odd Ns was carried out in the plot of the 1 /Ns dependence of δNs/J. Although the fitting gives the vanishing gap, treating data of even Ns and odd Ns together is not appropriate. Actually, one finds in Fig. 3 of the present study that the two sequences of data are different from each other.
20. M. Matsumoto, C. Yasuda, S. Todo, and H. Takayama: Phys. Rev. B 65 (2001) 014407.
21. A negative F is considered to come from the neglected higher-order terms with respect to 1 /Ns1/2.
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23. J. Schulenburg: http://www-e.uni-magdeburg.de/jschulen/spin/index.html
24. Reference 2 stated that an unpublished numerical-diagonalization result for the ground-state energy of the Ns = 42 cluster obtained by Andreas Lauchli is 0.43814, which agrees with our present result in Table I.
25. Unfortunately, there is insufficient memory in the supercomputer of ISSP to calculate the ground-state wave function of the Ns = 42 system at the present time, although we have successfully calculated only its energies.