Fermionic versus bosonic descriptions of one-dimensional spin-gapped antiferromagnets

Abstract

In terms of spinless fermions and spin waves, we describe magnetic properties of a spin-1 2 ferromagnetic-antiferromagnetic bond-alternating chain which behaves as a Haldane-gap antiferromagnet. On one hand, we employ the Jordan-Wigner transformation and treat the fermionic Hamiltonian within the Hartree-Fock approximation. On the other hand, we employ the Holstein-Primakoff transformation and modify the conventional spin-wave theory so as to restore the sublattice symmetry. We calculate the excitation gap, the specific heat, the magnetic susceptibility, magnetization curves, and the nuclear spin-lattice relaxation rate with varying bond alternation. These schemes are further applied to a bond-alternating tetramerized chain which behaves as a ferrimagnet. The fermionic language is particularly stressed as a useful tool to investigate onedimensional spin-gapped antiferromagnets, while the bosonic one works better for ferrimagnets.

Signature of the Luttinger liquid phase in alternating Heisenberg spin-12chains: Analytical and numerical approaches

“…9 By the above transformations, the AF-F spin chain is mapped onto a 1D system of interacting spinless fermions,…”

“…When these systems are placed in an external magnetic field, they can be mapped onto a 1D system of interacting spinless fermions ͑SFs͒. 1,[5][6][7][8][9] The filling of a fermionic band can thus be continuously tuned, making these systems suitable for probing the LL physics. 1,3,10,11 In the case of isotropic bond alternating AF-F spin- 1 2 chains, the whole band can be covered.…”

Thermodynamics of spin-1∕2antiferromagnet-antiferromagnet-ferromagnet and ferromagnet-ferromagnet-antiferromagnet trimerized quantum Heisenberg chains

“…In the conventional spinwave scheme, the spin deviations in each sublattice diverge in the one-dimensional (1D) antiferromagnets, but the quantum as well as thermal divergence of the number of bosons can be overcome in the Takahashi scheme [17] that will be applied to the present antiferromagnetic F-F-AF chain. The AF-AF-F chain is a ferrimagnet, whose magnetization should be nonzero in the ground state but zero at finite temperature, leading to that we can apply the Yamamoto scheme [21,22], where the Lagrange multiplier was introduced directly in the free energy, to our present ferrimagnetic AF-AF-F chain. The detail derivations of the MSW formalism are collected in Appendix A, where the linear modified spin-wave (LMSW) theory, which is up to the order of O(S 1 ), and the perturbational interacting modified spin-wave (PIMSW) theory, which is up to the order of O(S 0 ), are included.…”

Magnetic properties of the spinS= 1/2 Heisenberg chain with hexamer modulation of exchange

“…A particular realization of such a scenario appears in the one-dimensional (1D) space-modulated (alternating) quantum spin systems. The bond-alternating Heisenberg spin-1/2 chains which are obtained by a space modulation in the exchange couplings represent one particular subclass of low-dimensional quantum magnets which pose interesting theoretical [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and experimental [18][19][20][21][22][23][24][25][26] problems. The bond alternating spin-1/2 chains have a gap in the spin excitation spectrum and reveal extremely rich quantum behaviors in the presence of an external magnetic field.…”