References
- Majumdar CK, Ghosh DK. On next–nearest–neighbor interaction in linear chain. II. J Math Phys. 1969;10:1399–1402.
- Haldane FDM. Spontaneous dimerization in the S=1/2 Heisenberg antiferromagnetic chain with competing interactions. Phys Rev B. 1982;25:4925–4928.
- Tonegawa T, Harada I. Ground-state properties of the one-dimensional isotropic spin-1/2 Heisenberg antiferromagnet with competing interactions. J Phys Soc Jpn. 1987;56:2153–2167.
- Okamoto K, Nomura K. Fluid-dimer critical point in S = 1/2 antiferromagnetic Heisenberg chain with next nearest neighbor interactions. Phys Lett A. 1992;169:433–437.
- Allen D, Se'ne'chal D. Semiclassical description of the frustrated antiferromagnetic chain. Phys Rev B. 1995;51:6394–6401.
- Chitra R, Pati S, Krishnamurthy HR et al. Density-matrix renormalization-group studies of the spin-1/2 Heisenberg system with dimerization and frustration. Phys Rev B. 1995;52:6581–6587.
- White SR, Afflech I. Dimerization and incommensurate spiral spin correlations in the zigzag spin chain: analogies to the Kondo lattice. Phys Rev B. 1996;54:9862–9869.
- Mahdavifar S. Numerical study of the frustrated ferromagnetic spin-1/2 chain. J Phys Condens Matter. 2008;20:335230–335236.
- Matsuda M, Katsumata K. Magnetic properties of a quasi-one-dimensional magnet with competing interactions: SrCuO2. J Mag Mag Mater. 1995;140–144:1671–1672.
- Kikushi H, Ngasawa H, Ajiro Y et al. Susceptibility and high-field magnetization of one-dimensional S = 1/2 Heisenberg antiferromagnet with next-nearest exchange interaction. Phys B. 2000;284-288:1631–1632.
- Hosokoshi Y, Katoh K, Inoue K et al. Construction of a quantum-spin system of S = 1/2 antiferromagnetic chain with the next-nearest-neighbor interactions. J Phys Soc Jpn. 1999;68:2910–2913.
- Hagiwara M, Narumi Y, Kindo K, et al. High-field magnetization of an S = 1/2 zigzag chain compound (N2H5)CuCl3. Phys B. 2001;294-295:83–86.
- Okunishi K, Tonegawa T. Magnetic phase diagram of the S = 1/2 antiferromagnetic zigzag spin chain in the strongly frustrated region: cusp and plateau. J Phys Soc Jpn. 2003;72:479–482.
- Tonegawa T, Harada I. Magnetization curves in the ground state of spin-1/2 antiferromagnetic XXZ chains with competing interactions. Phys B. 1989;155:379–382.
- Schmidth M, Gerhardt C, Mütter K-H, et al. The frustrated antiferromagnetic Heisenberg model in the presence of a uniform field. J Phys Condens Matter. 1996;8:553–568.
- Gerhardt C, Fledderjohann A, Aysal E, et al. η-exponents in the one-dimensional antiferromagnetic Heisenberg model with next-nearest-neighbour coupling. J Phys Condens Matter. 1997;9:3435–3445.
- Cabra DC, Honecker A, Pujol P. Magnetic properties of zig-zag ladders. Eur Phys J B. 2000;13:55–73.
- Okunishi K, Hieida Y, Akutsu Y. Middle-field cusp singularities in the magnetization process of one-dimensional quantum antiferromagnets. Phys Rev B. 1999;60:6953–6956.
- Maeshima N, Okunishi K. Antiferromagnetic zigzag spin chain in magnetic fields at finite temperatures. Phys Rev B. 2000;62:934–939.
- Okunishi K, Maeshima N. Spinon excitation and Möbius boundary condition in S = 1/2 antiferromagnetic Heisenberg spin ladder with zigzag structure. Phys Rev B. 2001;64:212406/1–212406/4.
- Heidrich-Meisner F, Honecker A, Vekua T. Frustrated ferromagnetic spin-1/2 chain in a magnetic field: The phase diagram and thermodynamic properties. Phys Rev B. 2006;74:020401/1–020401/4.
- Okunishi K, Tonegawa T. Fractional Sz excitation and its boundstate for the S = 1/2 antiferromagnetic zigzag spin chain in a magnetic field. J Phys Soc Jpn. 2005;74:151–156.
- Oshikawa M, Yamanaka M, Affleck I. Magnetization plateaus in spin chains: “Haldane Gap” for half-integer spins. Phys Rev Lett. 1997;78:1984–1987.
- Lanczos C. An iteration method for the solution of the Eigenvalue problem of linear differential and integral operators. J Res Natl Bur Stand. 1950;45:255–282.
- Nakano H, Sakai T. Anomalous behavior of the magnetization process of the S = 1/2 Kagome-Lattice Heisenberg antiferromagnet at one-third height of the saturation. J Phys Soc Jpn. 2014;83:104710/1–104710/7.
- Nakano H, Sakai T. Numerical-diagonalization study of spin gap issue of the Kagome Lattice Heisenberg antiferromagnet. J Phys Soc Jpn. 2011;80:053704/1–053704/4.
- Sakai T, Takahashi M. S = 1 antiferromagnetic Heisenberg chain in a magnetic field. Phys Rev B. 1991;43:13383–13393.
- Nakano H, Takahashi M. A plateau in the magnetization process of the S = 1 spin chain. J Phys Soc Jpn. 1998;67:1126–1129.
- Totsuka K. Magnetization plateau in the S = 1/2 Heinsenberg spin chain with next-nearest-neighbor and alternating nearest-neighbor interactions. Phys Rev B. 1998;57:3454–3465.
- White SR. Density matrix formulation for quantum renormalization groups. Phys Rev Lett. 1992;69:2863–2866.
- White SR. Density-matrix algorithms for quantum renormalization groups. Phys Rev B. 1993;48:10345–10356.
- Shahri Naseri M, Mahdavifar S, Farjami Shayesteh S. A novel plateau in the magnetization curve of the alternating Heisenberg chain. J Supercond Novel Magn. 2010;24:735–739.
- Shahri Naseri M, Japaridze GI, Mahdavifar S, et al. Magnetic properties of the spin S = 1/2 Heisenberg chain with hexamer modulation of exchange. J Phys Condens Matter. 2012;24:116002/1–116002/12.
- Zhitomirsky ME, Honecker A, Petrenko OA. Field induced ordering in highly frustrated antiferromagnets. Phys Rev Lett. 2000;85:3269–3272.