Spin Chain in Magnetic Field: Limitations of the Large-N Mean-Field Theory

Motivated by the recent success in describing the spin and orbital spectrum of a spin-orbital chain using a large-N mean-field approximation [Phys. Rev. B 91, 165102 (2015)], we apply the same formalism to the case of a spin chain in the external magnetic field. It occurs that in this case, which corresponds to N=2 in the approximation, the large-N mean-field theory cannot qualitatively reproduce the spin excitation spectra at high magnetic fields, which polarize more than 50% of the spins in the magnetic ground state. This, rather counterintuitively, shows that the physics of a spin chain can under some circumstances be regarded as more complex than the physics of a spin-orbital chain.

[1]  J. van den Brink,et al.  Orbital control of effective dimensionality: from spin-orbital fractionalization to confinement in the anisotropic ladder system CaCu(2)O(3). , 2013, Physical review letters.

[2]  A. Oleś,et al.  Topological order in an entangled SU(2) ⊗ XY spin-orbital ring. , 2013, Physical review letters.

[3]  H. Rønnow,et al.  Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain , 2013, Nature Physics.

[4]  P. Horsch,et al.  von Neumann entropy spectra and entangled excitations in spin-orbital models , 2012, 1206.1062.

[5]  J. Brink,et al.  Spin–orbital separation in the quasi-one-dimensional Mott insulator Sr2CuO3 , 2012, Nature.

[6]  W. Marsden.  I and J , 2012 .

[7]  J. van den Brink,et al.  Intrinsic coupling of orbital excitations to spin fluctuations in Mott insulators. , 2011, Physical review letters.

[8]  M. Kohno.  Dynamically dominant excitations of string solutions in the spin-1/2 antiferromagnetic Heisenberg chain in a magnetic field. , 2008, Physical review letters.

[9]  W. Brenig,et al.  Spin dynamics of the antiferromagnetic spin-1/2 chain at finite magnetic fields and intermediate temperatures , 2008, 0811.1956.

[10]  C. Batista,et al.  S=½ chain in a staggered field: high-energy bound-spinon state and the effects of a discrete lattice , 2005, cond-mat/0503135.

[11]  T. Pruschke,et al.  Quantum cluster theories , 2004, cond-mat/0404055.

[12]  G. Muller,et al.  Quasiparticles Governing the Zero-temperature Dynamics of the One-dimensional Spin-1/2 Heisenberg Antiferromagnet in a Magnetic Field , 2002, cond-mat/0205142.

[13]  Perez,et al.  Spectral weight of the hubbard model through cluster perturbation theory , 1999, Physical review letters.

[14]  Fu-Chun Zhang,et al.  Ground state and excitations of a spin chain with orbital degeneracy , 1999, cond-mat/9902269.

[15]  Nj,et al.  DIRECT OBSERVATION OF FIELD-INDUCED INCOMMENSURATE FLUCTUATIONS IN A ONE-DIMENSIONAL S = 1/2 ANTIFERROMAGNET , 1997, cond-mat/9704034.

[16]  A. Auerbach.  Interacting electrons and quantum magnetism , 1994 .

[17]  I. Affleck,et al.  Large-n limit of the Heisenberg-Hubbard model: Implications for high-Tc superconductors. , 1988, Physical review. B, Condensed matter.

[18]  H. Thomas,et al.  Quantum spin dynamics of the antiferromagnetic linear chain in zero and nonzero magnetic field , 1981 .